This is a tricky situation because every broody hen is different. That makes it hard to predict what will happen.
I can tell you some of the experiences I have had with my broody hens. I have 2 hens that are on the same brooding schedule, and I always have them brood together. I normally split a dozen eggs between them. They have separate broody houses, but are kept in the same pen. It works out great with those two ladies. They share responsibilities, and make an excellent team.
Then one time I had several broodies hatching together, again in separate broody houses, like little doghouses, but all in the same pen. One hen was simply awful! She beat up all the other hens and stole their babies. It was the saddest thing! Not only was there blood and feathers everywhere, there were some sad and forlorn hens who desperately wanted their babies back, but weren't tough enough to take them. I ended up putting the most docile hen in broody jail and breaking her of her broodiness, then separating out the other hen and giving her some of the babies. I have no idea if they were her original babies or not, but she didn't care.
So, I've never had a broody hen try to harm another broody's babies. But that doesn't mean it can't happen, just that it's never happened here. One idea that I can think of is this: When your broody that is currently sitting hatches her eggs, you might move them into some sort of a dog crate for a few days. That would give the hen and chicks time to bond, and also give the chicks time to get steady on their feet, in case they need to run away from the other mother hen. Also, the other hen would have a chance to get used to the idea of another set of chicks in her area.
If you have no place to separate the two mothers, then that's just the way it is. So be watchful at first, and try to think of what you will do if things turn ugly. It's possible that they won't. Sometimes it works out well. Like with my Sugar and Blondie, the amazing broody duo. I love having them raise chicks together. But it really all depends on the personalities of the hens in question.
Good luck!