You have aggression issues by the sounds of that, and they're dictating to you how you manage your flock. Even having one of your hens raise chicks among the flock is not going to fix that, they will attack them as well.
I cull against aggression personally, I've tried to manage it but it was never worth the time and effort, and culling solves that problem completely. I get that's possibly not an option for you, but if your old layer flock needs numbers bumped up to keep production up, but is too aggressive to add more to, personally I'd cage the lot of them separately and begin a new flock from scratch, and select against aggression in this new flock. Your job becomes so much easier when you don't have animals with vicious temperaments to manage. Not to mention their quality of life is better and they're more productive because they're less stressed. Although chances are by the sounds of it your older layers would tear one another to shreds if caged together...?
Your broody hen was never going to be a good mother I reckon, not if she has a track record of regularly cutting off so early, that's a surefire indication that she's lacking the necessary strength and detail of instinct. She would almost certainly fail to successfully mother any chicks you give her, and to give her such an opportunity I would expect to be about as useful as throwing chicks to the dogs. The same trait that causes them to prematurely break off the brood is generally linked to also breaking off mothering without warning. It's a sudden hormonal reversal to non-maternal condition and behaviors, which in a good mother only happens gradually and over a period of weeks, not in the space of a few minutes or hours.
Maternal instinct is a spectrum of behaviors etc, not a single box to tick... I'm guessing you know this, but I got the (perhaps incorrect) impression you'd still try her out if she sat for long enough, and I think it'd be a failure and a waste of chicks' lives.
Sitting on eggs and being nest-defensive doesn't prove she has the ability to mother, just that she has some of the hormonal drive to brood. Her extreme aggression to you is not a good sign unfortunately, it means she's more likely to harm the chicks in her overriding drive to attack than to actually mother well.
I used to think strong nest-defensiveness and protective aggression were good signs, but experience only proved otherwise. I ended up culling that mentality out because it did destroy whole clutches and my best mother hens never had those traits.
I had one turkey hen that would start scratching at the ground like a bull pawing the dirt when she saw me approach, crippling her chicks as she did so; she was just completely obsessed with attacking me, not a single concern for the babies' welfare, no reaction to their screams as she damaged them --- except to become angrier at me. She did appear to blame me for what she did to her own babies and with every death she became more enraged at me until she was eventually too dangerous to get into a cage with.
I had one chicken hen (a little bantam) that bit savagely like yours, she would leave marks like a pair of wirecutters, with internal bleeding. I tried showing her no reaction so she got no reward for it, but she wasn't fooled and would then get in between the fingers to try to cause maximum pain, and bite on and twist; when she realized her biting wasn't going to chase me away, she started to fly my face. She'd also trample babies because what was more important to her was attacking me, not looking after them. Nothing I could do would change her mentality, as with the turkey and other aggressive animals I've had, I tried everything in the book and invented some things too.
She was only a tiny bantam but man could she pinch! I'd end up with purple/blue 'V' marks everywhere. She'd start amping up into a state of extreme aggression as soon as she saw me coming on my daily rounds with the food and water, and by the time I arrived she'd be just psychotically enraged, smashing herself into things to get to me, and her babies would be running back and forth in distress, because such mothers do really distress the babies.
Hens like her, and like yours, I've found, tend to maul babies if you handle them, just because you touched them. If it's in your hands they will rip it up. That's a problem if you ever need to handle the chicks in front of them. They'll also smash eggs in your hands. Strong aggression is not useful at all.
You don't really want a nasty animal rearing chicks anyway I reckon, they can and do lay down some very strong inclinations in the chicks to avoid or attack humans like predators. I've had hens fail at every possible part of the task of mothering, no matter how good they were at any other aspects of it. Given my experiences I would absolutely not give that hen of yours a chance as a mother, she sounds like a guaranteed dud.
Here's some of the examples of incomplete maternal instinct, or maternal failure, that I've seen. I expect your semi-broody would fit into one of these categories, most likely multiple because that seems to be the way it goes, they very rarely screw up the job in only one aspect of it. Most of these failure types I've seen many examples of, but there's always more examples showing up the longer I keep chooks. These are common failures:
- Incomplete brooding (like your hen shows) is obviously a failure that kills eggs; I never let them go any further with it because they are clearly severely unreliable and giving them chances in the past was a waste of time and a mistake.
- Incomplete brooding --- perches at night like normal, only broods during the day.
- Incomplete broody instinct, often leaves eggs sitting in front of her (fails to roll them under her or gather them) --- ends up with a lot of dead eggs because of that.
- Broods fine --- then kills all the chicks when they hatch. Some just repeatedly bash between the shoulderblades and you later find paralyzed and dying chicks, often without knowing why as there's no sign, besides drooping wings and (maybe) some mild swelling. One hen I had brooded perfectly, but when the chicks hatched she ate just their eyes and brains.
- Broods fine, bonds to the chicks --- then refuses to leave the nest until the chicks eventually abandon her because they're starving, or worse, sits there till the chicks die of dehydration. Another way a hen can fail like this is just not teaching the chicks where the food and water are, and to go to them regularly. They can die of want in the midst of plenty.
- Broods fine --- but as soon as chicks hatch, is offended at the destroyed eggs they hatched out of, leaves the chicks and find another clutch to sit on, completely ignoring their cries (no bond).
- Broods fine --- but is completely unable to stop brooding, because nothing you can do will stop her and she can't stop herself, the hormones are unable to cut off normally. Broods nonstop for many months until she dies.
- Broods fine, vocally responds to the chicks --- but at hatching, if you check on them late at night, you'll find that hen standing above the eggs, letting the hatching chicks chill to death at this crucial time.
- Broods fine, bonds to them --- but doesn't 'talk' to them, or perhaps only makes 'angry noises' if she does vocalize --- so they don't have a sure bond to the mother and have to try to play it by sight alone, which they cannot satisfactorily do, leading to them having to experiment with finding their own food and water, getting lost and attacked for following the wrong chickens, and generally failing to thrive due to maternal neglect.
- Broods fine, bonds to them --- but doesn't tell them where food or water is, just walks around clucking meaninglessly and ignoring their increasingly desperate cries. Takes care of herself but not them despite associating with them.
- Broods fine, bonds to them, tells them where food and water are --- but doesn't snuggle them, so when she decides (for example) that it's time for an early morning roam across a frosty paddock, the sodden and seriously chilled chicks' cries are ignored; where a good mother would interpret the cries correctly, stop and crouch to snuggle them and reheat them, this type of mother just keeps walking. If she does react at all it's usually with anxiety and a faster walking pace.
- Broods fine, bonds to them, feeds/waters/heats them --- but abandons them without warning long before they are remotely able to cope without her.
- Broods fine, bonds to them, feeds/waters/heats them --- but is so human-averse she teaches them to respond to you like a predator, and flee from you in panic, or attack you. Good luck ever taming the adult results of that maternal mentality.
Once I learned what the warning signs meant, I never let hens showing any deficiency of maternal instinct ever try again. Some people are content to let hens waste clutch after clutch 'learning' but I just ate these hens or kept them as layers and repeatedly broke them off the brood as necessary. What a ridiculous waste of time, effort, and lives such hens are when one tries to use them in maternal roles.
If your flock is cramping and controlling your purpose for them, or their usage and usefulness, change them to suit you, not change to suit them, I suggest.
You only have to put up with what you keep and breed. Not all chickens are aggressive at all, it's more a family trait rather than a breed trait, and certainly not inherent to the species. It's entirely possible to have a completely aggression-free flock, if you just cull out aggressive animals. I'd eat this semi-broody, myself, and get in some proven broodies and put them to use.
Best wishes and good luck with them.