Do we need to separate her and her chicks from the others or will she be able to handle other adults around her chicks?
Before they were domesticated broody hens were raising chicks with the flock with no influence from humans. They did not go extinct. That does not mean there were never any issues with other flock members but they did not go extinct. Those issues were rare.
After they were domesticated things changed for some chickens. Many continued to free range with minimal influence from humans, but some people started feeding some instead of letting them feed themselves and started keeping them in coops and runs, thus restricting their movement. We started selective breeding, one result being that many hens no longer go broody. The ones that do go broody still generally have the instincts for them to hatch and raise chicks but they don't always have the freedom to act on those instincts. They are restricted to coops and runs.
All this leads to one question, "What do your facilities look like?" If the broody has room to work she can usually do a great job in raising the chicks from hatch until she weans them. Usually, you do not get guarantees with living animals. If they have enough room the chicks can usually do a great job of taking care of themselves after the hen weans them and until they mature enough to join the pecking order. I'm not talking about any minimal square feet per chicken. What counts is can they get enough physical separation during the day and at night to manage.
If you can describe your facilities and your flock I'll give you my opinions and maybe suggestions. What I'm basically looking for is size of the coop and the run in feet and what they look like, including inside the coop. Roosts, nests, is it elevated, and such. Photos can really help.
We also have 2 female ducks that have lived with the chickens forever. Will they become a problem? They were raised together from hatchlings. And we have two roosters. All of them share the same area.
If they have enough room this usually works out but I don't give guarantees on behaviors of living animals.
Do we need to add extra warmth in some way
Absolutely not. Hens can raise chicks with snow on the ground.
or feed the chicks somehow separately (we use an all flock food right now and supplement oyster shells some).
With all-flock and offering oyster shell on the side you are OK. I suggest widely separated multiple feed and water stations so the chicks can eat and drink without being bullied, especially after the hen weans them.