I understand your first time with a broody is nerve-wracking but after you gain a little experience with them you'll appreciate how well they do and how tough those chicks are.
Where are you located? How cold are you talking about? Broody hens typically provide all the heat the chicks need, even down to freezing. The chicks eat and drink, then go under her to warm back up. I'm not sure you are doing them any favors with that heat lamp. I have nothing against a heat lamp as long as they are properly secured but I doubt it is really necessary.
I let my broody hens hatch with the flock and raise the chicks with the flock. It's never been an issue but I have a lot of room. I agree that the hens are generally more of a risk than a mature rooster. Occasionally my mature roosters may help the hen with her chicks but most just ignore them. Most hens aren't a problem either. When a hen threatens a chick the broody kicks butt. I don't have experience with ducks but fencing them out is probably a good idea.
How much age difference will there be between those incubator chicks and the broody's chicks? The closer they are in age the more likely it is the hen will adopt that chick. If it is 2 or 3 days the dds are pretty good. After that it is more problematic, but may be possible.
If you do try to isolate the broody and chicks, do a good job of that. Make sure the chicks cannot get through a barrier so they can get away from the broody hen's protection. They are at risk if she cannot protect them.
Whenever I've had chickens hatch out in a nest box, some of the chicks do manage to fall or jump out.
Could you please post photos of your nests. My hens hatch at elevation all the time and only once has it been a problem. The problem was the nest, not the height.