In my one time experience mixing cockerels with chicks, there was no danger to the chicks. And I had
three 4 month old cockerels when the last two broods hatched. The mothers were so terrifying to the cockerels, they just avoided the broods.
The potential problem is when the mother starts weaning the chicks and coming back into lay. She will start flushing red with egg producing hormones and the cockerel could take it as an invitation -- which it is, biologically -- but might invite him to be rough with the mother hen. But not the chicks.
If the mother starts returning to lay BEFORE she has completely weaned the chicks, she could hesitate in running away from the hormonal cockerel, and that will increase the cockerels mating attempts. Cockerels are clumsy at mating and more likely to cause injury to hens.
The presence of an older rooster might keep the cockerel in check, but even if the rooster runs off the cockerel, he may grab the hen himself to "prove" she is "his." That's what Lucio did anyway.
Roosters are like cavemen, in my experience, seriously. They might be gallant and brave when it comes to offering treats and protecting from predators, but when it comes to mating and showing "these women are MINE" they are quite uncivilized. Which is fine. They are what they are. But be prepared.
These factors contributed to my little Dusty's injury. She started flashing red/coming back to lay only six weeks after her chicks hatched. She was still spending time with her chicks, and when the cockerels chased her, she didn't want to run away from her chicks and got caught too many times. The cockerels were 5 months at that point and their transition from cute hooligans to full-fledged gang of hoodlums was FAST. I got two of the cockerels out to new homes within two days of these mating frenzy pile-ons, but poor Dusty was hurt.
She is still recovering and I've been having to clean and dress the wound on her back daily. It was healing fine, but then got infected under the scab. Two days ago, I removed the scab, scraped out all of the nasty pus that had formed under it, flushed and disinfected. The inflammation has subsided and she's on a short course of antibiotics just to be sure because the wound is deep and bacteria can take hold again. I think she will be fine eventually, but she shouldn't have had to go through that. It was my mistake to let the cockerels stay so long in a free-range anything goes situation.
That will not happen here again.
Fortunately Dusty went broody (again) and I gave her eggs to set. Her chicks are almost ten weeks. I usually wouldn't let a hen hatch back to back clutches, but I figure this is the best way to keep her away from Lucio and Tobias and give her time to heal while she is contentedly sitting on eggs.
Other than the gash on her back, she's fine. She has full movement in her wings, no stiffness, fever or necrosis, she gets of her nest, poops, eats, drinks and goes back. I think her prognosis is good, but to get back to your question--
In all, I don't think cockerels pose any danger to chicks. But they can be dangerous to mothers in the transition between weaning and coming back to lay. Granted, you don't have three horny devils and I think you have some sort of partial confinement circumstance, but I'd make sure the mama doesn't get roughed up if she starts flashing a red face and comb while she's still tending to her chicks.
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Dusty, back in the broody zone.