Mom's usually do this when there is something wrong with the baby. The baby eating is a good sign though. I had a friend that the Mom would bring the tiny baby to him for help. He started supplementing the little one, and Mom would bring him the baby every time she thought it needed fed.
I would put her and the babies in an X-pen. What would be worse than a sick baby passing, would be you rolling over onto it in bed and not waking up.