It is perfectly ok to take the chicks from the mom if you have to, it won't hurt them or her. Lots of people raise their chicks without a hen at all. But, it is easier and more natural for them if you can have the hen do it, so I'd agree with moving her and them both to their own pen. Chick eating can be a problem; when I had chickens growing up they would eat every chick they could get ahold of! We built a brooder pen inside the coop, and the hens would break it apart to eat the chicks inside.
If you don't put mama in with them, they should have a heat lamp to keep them warm. Also, give them chick food and water; they will begin eating within a day or so of being hatched. They can go up to three days without food because they absorb the egg yolk into their bodies, but if given food, they will usually eat within the first day or two. Also, if you give them water in just an open dish, make it shallow and put rocks or marbles in it so that they can drink but cannot accidentally drown in it; chicks drown easily.