It's not clear to me. Will the older hens have their own separate pen? Will the 4 week olds have their own pen? If so, then things should work out fine with the younger chicks.
If you are very cautious, it would be easiest if the lone chick that was with the mom has the home court advantage of being in the coop by herself (girl or boy). Then on the first day, add one new chick and let them become buddies. Then add another the next day or maybe two. Keep the same feeder and waterer that the lone chick was used to because it will be a transition because momma always told her what and when to eat. Once the lone chick has gotten used to having other chicks around and is getting to the feeder and waterer without trouble, then you can add in the others. It can go more quickly than that, but you just have to play it by ear. I'd probably try to do it all in a day. But some will depend on if the first two know where to go to be at night and will do so. The new chicks will follow the others to bed (probably or hopefully). It is no fun putting chicks new to a coop to bed one by one in my grow out coop because the run is 4 feet high and I have to crawl on the ground. But your set up will undoubtedly be very different.
Yeah, I know you might have to buy another brooder set up. A back up set up maybe would be useful anyway? But at 4 weeks, there's a really good chance that it will be super easy and you won't need another set.
I think I would start just before dawn and move the broody momma off to the laying flock's coop because she won't be too happy at first and if it's dark she'll be easier to handle. She may mope around for a few days.
Seriously, though, 4 week old chicks rarely notice a new chick in the group. None of mine have paid much attention as long as the chick blends in color-wise and doesn't have a crest. I put a couple silkies into a group of three and four week olds just recently without a hitch, not even the crests were a problem. But I've had a little trouble when everyone is older and they're more worried about pecking order.
Anyway, that's my 2 cents. Everyone does it differently and has different experiences.