Many of us let them mingle as soon as Mama brings them off the nest. You are dealing with living animals so no one can give you a guarantee, but I have never really had a problem doing this. Most broodies are really protective of their chicks and while the adults are likely to be curious about the new members at first, most won’t go out of their way to attack the chicks. It sounds like you have plenty of room, which helps.
One of the reasons I like the broody to raise the chicks with the flock is that she takes care of basic integration. When she weans them they still have to deal with pecking order issues on their own, but they will just avoid the older chickens until they mature enough to establish their position in the pecking order.
As long as Mama is still broody, she will protect her chicks and teach the rest of the flock not to harm her babies. I’ve had a broody wean her chicks at three weeks, which is pretty unusual, with 4 to 9 weeks fairly common. I like Mama having as much time as possible to teach the others to leave her babies alone.
So when can you let them mingle? Whenever you wish.
The Layer presents another problem. As you probably know, growing chicks should not eat Layer. Here are a couple of studies that show what happens to chicks that are fed nothing but Layer, one starting at hatch and one starting at 5 weeks. It’s the calcium that causes the problems. Not only do they count the number of chicks that just die, they cut the chicks open to see the damage done to their internal organs.
Avian Gout
http://en.engormix.com/MA-poultry-i.../avian-gout-causes-treatment-t1246/165-p0.htm
British Study – Calcium and Protein
http://www.2ndchance.info/goutGuoHighProtein+Ca.pdf
Something to note about these studies. The chicks are fed nothing but Layer or Layer equivalent. One bite won’t kill or harm them. It’s how much total calcium they eat in the day, not how much calcium is in one bite. And it’s not about how much total calcium they eat in one day, but it’s a cumulative effect over several days.
You can’t keep those chicks out of the Layer. Mama will take Layer out of the feeder and give it to her babies. At one week old, my chicks fly up into the adult feeder to eat their fill.
If the majority of what they eat is not Layer but is from them foraging, which is real likely from how I imagine your set-up, the Layer they eat will probably not be enough to harm them. Again, that depends on what they are foraging on. They can pick up extra calcium from certain plants, critters, or maybe even the bits of rock they use as grit if it is limestone. So to me, letting them be around Layer is not a good practice. You really don’t know if they are going to eat enough to harm themselves or not.
The traditional way around this dilemma on this forum is to feed them all Starter, Grower, Flock Raiser or something else that is fairly low in calcium and offer oyster shell on the side. The ones that need the extra calcium for their egg shells seem to instinctively know they need to eat it and the ones that don’t need it won’t eat enough to harm themselves. You are dealing with living animals so you can always find an exception, but this system works for the vast majority of us.
Hope this helps. Good luck and congratulations on those chicks. There is just something about watching a broody taking care of her babies.