They need to be in a room alone with their mother. I look after many stray cats - mums and kittens, particularly in the summer - and the very best we can do for them is to give them a room of their own in complete isolation. Set up a bed for them - a cardboard box on it's side is ideal - with plenty of towels and blankets for them. Mum will of course need her litterbox. Food and water left down won't be eaten by the littens themselves if they're still very young, so it's not a problem if she moves them away from it. She is less likely to move them around if she feels safe in a room alone with them. It could be that she moves them because she feels that there is a threat. She sounds like a first-timer as well, and that can be really stressful for her in itself. Some of our first-time mums will even walk away from them because they simply don't know what to do with the kittens. But given a little peace and quiet, she may come around and her maternal instincts may kick in and she'll do better. Obviously you should try and pet her often, and handle the kittens, just so that she and the kittens get to know your smell and will feel safe with you. But it is important that you never disturb her if she is feeding them, because that can disrupt the feeding pattern and they won't get as much nourishment as they really need.
I hope this helps a little - I'm just relating my experiences with mothers and kittens, but I know there is a wealth of info out there