With our broodies, we move them from the nest box to a broody box in the coop after all the eggs (that are going to hatch) have hatched. It's open so she decides when to take them out. Generally they stay in the box a day or so after the hatch, then bring them out into the coop to scratch around for a couple of days. After that, they stick close to the coop but do venture outside. We let the mama do all the work, but we keep an eye peeled and make sure no chicks are being rejected. We've had 2 broodies so far since late April and have one more sitting on 4 eggs, and every mama has been fierce in protecting her babies. None of our flock has been deliberately mean, thank goodness, but even if they are foraging too close they get walloped by the mama. Personally, I would do it as you stated in your post- leave the crates open and let them decide, but do try to watch and make sure everyone is getting along. My experience is different because I've never had 2 with chicks at the same time.
I have a batch of 5 chicks that are about almost 8 weeks old. Their mama stopped mothering them a couple of weeks ago and they have done pretty well. I left them in the coop and with the flock so I wouldn't have to do the integration, and so far it's ok. Not to say they don't get pecked by the adults, especially at night when trying to roost, but they're figuring it out and no one is being anything other than I expected. They have to learn the rules of the flock, and as long as no one is getting injured, I leave them to it.
