I don't know if it would work if you gave the new chick to the hen with the 4 week olds. Even if they accepted it, I personally wouldn't think the new chick would be able to keep up. I hope that someone with more knowlege posts soon.
We have an only chick that lives in the house and so far it has worked out. We take it outside everyday to see the older chicks under supervision only. When they get to be close to the same size, we will try combining it with the others.
That is a problem. I would not give the chick to her. There is a pretty good chance she will not accept it and protect it. She might kill it. The other two chicks might harm it. But the main reason is that it would probably confuse Mama.
With chicks four weeks old, if she is not taking them to the roosts now, she will soon. The baby could probably not go up with them for the first week or two. I've had hens take chicks to the roosts at 2 weeks, but that was during really warm weather. With cooler weather, a chick that young may be in trouble if they try to roost.
When would Mama wean them? I've had hens wean chicks anywhere from 3 weeks old to 9 weeks old. The broody is probably considering her options now. Would she postpone that for a new baby? I don't know.
Some broodies would probably accept it and do well by it, but I would not feel good about the chances of that happening.
I had a broody this summer, the eggs were bad and I slipped 4 day old chicks under her, all went well, but I lost 2 to pasty butt. I bought 2 more chicks, that were about a week old, 3 or 4 days older than the 2 under her, just enough age difference, at least a I think, that she wouldn't accept them. Wasn't totally mean to them, they were able to sleep under her for a couple of nights, but during the day, she would herd her 2 chicks away, and wouldn't let the 2 newcomers eat or drink water, so I had to remove them.