Need advice on mixing flocks of different ages

I currently have 5 hens (2 ameracaunas, 1 rir, 2 golden comets) who are about 1.5 years old. A few months ago, one of my golden comets went broody and I got fertilized eggs from a neighbor and some from my mom and she hatched 6 chicks. They are 7 weeks old today and have been outside, in a separate coop with mama hen since the day they hatched. The babies are 2 leghorns (I believe there's one rooster and one hen), and 4 buff bhrama/buff orphington mixes (and I believe 1 of those is also a rooster).
I've let both groups out to free range and there haven't been any major issues. One of my older girls actually prefers to stay with mama and the babies. The other 3 keep their distance but the 2 golden comets have chased each other a few times. No blood or missing feathers...I believe just pecking order, protective mama type stuff.
Anyways, their coops are side by side and I had planned on opening the runs to combine them as one big run and still having 2 different coops since I can't really add onto the coops the way that I have them.
So, here's where the problem comes in. My son brings home a slip from school to bring home some leghorn chickens they're hatching in class. To be fair, I filled it out saying I would take 3 because last year, my daughter brought home a slip and I also said we'd take some. We live in a rural farming area and there weren't enough chicks last year so we ended up not getting any from my daughters class. My sons slip said first come, first serve depending on when the papers were handed in. He handed his in on the deadline so I thought for sure, we weren't going to get any. So...teacher calls me this morning and asks if I can pick them up tomorrow.
So, we've got both coops filled currently. I doubt mama hen would take on additional babies at this point and it's really too cold for them to be outside now so I'll keep them in the upstairs bathroom under a heat lamp.
How should I go about eventually introducing these new babies? And really....why wouldn't they have waited until it was warmer to hatch chicks in school?
I do plan on getting rid of a few of the babies we have now. I had told my boyfriend that we were maybe keeping one or two but that it would be nice for the kids to see babies hatched.
So, what would you do to make this go as smoothly as possible??

 

Thanks for your reply! Kids sure do have a way of complicating things, lol.

My original coop was bought as a coop that could house "up to 10 chickens" but we were comfortable with it housing our original 6 hens and 2 guineas. The guineas died early on and we didn't replace them and a raccoon got one of our hens. I'd feel comfortable housing 8 full size birds in there. The second coop was built right next to the original coop and was made to house 4 muscovy ducks (that I have since butchered). There aren't any nesting boxes in there but that could easily be changed. The runs could easily be combined as a large run while still keeping 2 different coops accessible. That was kind of our quick fix plan until the spring when we could make a larger coop that could house a flock of 15 or so birds.
We've had chickens for about 1.5 years and had planned to replace the entire flock every other year so we never really planned on having more than 6-8 but.....that was a compromise with the boyfriend. He has now discovered how awesome chickens are and is on board with this farm raised girl to have more haha We just really didn't plan on needing to rearrange everything right before winter.
I think I've decided to rehome 4 of our babies (just keeping 2), and merge them into the flock in the main coop along with mama.
Big kid who wanted to bring home the babies will keep them in his room and be responsible for them until they can go outside.
I guess we'll work on making the run bigger so they have lots of room to run around. We are going to cover part of the run with thick plastic to keep the draft and snow out so even in the winter, they'll have dry ground to explore.

 

Well, tonight I took 4 of our babies and gave them to a friend down the street. I let the mama and her remaining babies free range with the older flock. I was gone longer than I had planned and it was dark when I got home. I went out to make sure they had made their way back to the coops and mama was in the main coop, along with the other 4 hens, with her 2 babies tucked under her wings. They all went in and found their spot on their own. And she didn't seem panicked when I took the 4 babies away. I had them in a box on the porch and she could hear them chirping but she kept going about her digging.
We'll see how they do in the morning since they'll all be in the run together. I've got a good feeling.
And our 3 new, new babies are set up in my sons bedroom. They'll be hanging out up there for several weeks.