Claiming to hold a lot more chickens than it actually will is pretty typical for online purchased coops and runs. That space is not even close to space for ten hens. It’s tight for four hens if they are left locked in there for long periods of time. I’m assuming you got the 3 meter run which they advertise for $1700. Here’s what I think you have.
https://www.omlet.us/shop/chicken_keeping/eglu_cube/
First stop locking them in there when you don’t have to. You don’t need to micromanage their diet, they can manage quite well on their own. Does this behavior occur when they are not locked up? Maybe something as simple as this can be the solution. You never know until you try.
I’m still not sure if she is truly broody or just hiding. I’ve had plenty of hens that will growl when I reach under them if they are just laying an egg, no broodiness involved. Normally when a broody is off the nest she walks around fluffed up and pocking, pretty much warning the other chickens she’s in one of those moods so leave me alone. Since this behavior just started two days ago broodiness might have something to do with it but I’m not convinced.
Many people can keep RIR and Sussex together without problems. With the space you have for them in the netting I’d really expect you to be OK, but obviously you are not. Sometimes you get chickens that are just aggressive for whatever reasons. Did something change two days ago in how you manage them or have you always locked them up at the start and end of the day? Something triggered them to start attacking her two days ago, I don’t know what. But now they are in the habit of attacking her so you have to deal with it.
Does one of the RIR initiate the attack with the other following? Is there any way you can isolate one RIR hen from the flock for several days, hopefully the aggressor, maybe in a dog crate? It does not have to have a lot of room. Does removing one hen alter the behavior of the other RIR? Sometimes removing one hen for a while and then returning her can alter flock dynamics enough to solve these problems. Sometimes. Or maybe you are destined for a three hen flock, or maybe just two.
Assuming she is broody, can you rig up a broody buster? That’s a crate with an elevated wire floor so her bottom can cool off. It needs to be predator proof. Give her food and water but nothing that looks like a nest. Usually a broody will break from being broody after three or four days in something like this. Doing something like this can be challenging for a lot of people, especially in suburbia.
I’m not at all convinced this behavior is due to a protein deficiency. You can stop that mug full of scratch if you wish but I don’t think that is enough to alter their behavior. You can ask at the feed store for a feed higher in protein. The protein content should be on the label. I’m guessing you are somewhere that when you say grit, you mean soluble grit, like oyster shell. In the US when we say grit we mean insoluble grit like granite. That’s often a language trap on this forum since we are worldwide. The higher protein feed will not have the amount of calcium the hens need for the egg shells but if you are offering insoluble grit (oyster shell) that’s OK. They should get enough calcium from that for their egg shells.
I’m kind of at a loss for any other suggestions. I haven’t dealt with anything quite like this.
Are two hens too few for companionship? Not really but you run the risk of something happening to one so you only have one left. I’d really like a minimum of three but a flock of two might work for years.
One problem with those facilities is that you are not set up great for integration. Ideally you would house them side by side with a wire separation for a week or so before you let them out together. A lot of people don’t do that though, they just toss the new chickens in with the old and see what happens. Often that works out fine. There is often a difference in “ideal” conditions and conditions “I deal” with. You may be in one of those situations.
Quarantine is an issue. You’ve seen how chickens can come in with problems. Usually those are more of an inconvenience than a serious problem, like worms or mites, and you’ve already shown you can manage those. But it is possible you could bring in something that would endanger the life of your flock. It’s also possible you will not bring in anything new. It’s a risk I’d probably take in your situation. The risk of actually losing your flock is pretty low, but there is a risk.
If she is truly broody you could get hatching eggs, maybe even from that breeder. I could easily see you setting up a broody enclosure in that covered run (or maybe get rid of the two RIR’s and let her hatch in a normal nest), but you don’t know how many will hatch or how many will be pullets or cockerels. You need a plan to deal with cockerels and be able to handle the number of pullets you get.
I’m sorry you are having all these problems. With your set-up and space you should be able to have four hens without any real issues. All that space in the netting should really make life easy for you. I really don’t see that you are doing anything wrong, I think you have just had some bad luck. When you deal with living animals that sometimes happens.