Last update -
Chicks are about 5 weeks old. They are fully integrated into the flock.
Mama hen still chases the other hens away from her chicks, which means that they leave the other 4 chicks alone too. Mama took her babies into the coop to sleep last night and this morning couldn't get away from them fast enough. She also laid her first egg in 7+ weeks. The four brooder chicks hang out together and the two that were mothered don't really interact with them much but I assume that will change as the mama leaves them.
One of the mothered chicks is a surprise rooster and he is not very happy about being abandoned. He cheeps at the mama whenever she gets too far and she ignores him. It's pretty funny. The other chick doesn't seem to mind.
I feel like I got really lucky - for those reading this who might want to do the same. Several factors helped. First my broody was the top hen, and the others follow her lead. They are staying away from all thare chicks, not just the mama hen's two.
Second I spent a lot of time with them while I was integrating them. I acted as the "mom for the four and my mama hen definitely trusts and respects me.
Third I had a lot of space to keep them separate but near each other- I had a coop, a broody pen in a connected shed, and then a portable puppy playpen for the 4. I have electricity in my chicken coop for the brooder plate so I could move them out there pretty young and they would stay warm enough.
I do think having the broody raise a couple also helped with integration rather than brooding them all separately. I got super lucky that I had a broody at the right time and she was so good at it. Without her I think I would have had to wait until the chicks were much bigger to integrate the two groups.
Thanks for all of your advice and I hope this thread helps others someday
Here are the four sunbathing in the run - two Delaware, a Swedish Flower hen and a golden cuckoo Marans.