Yes, some of the nail paint removers are safe to apply to children even if they are infants. You must look at the package before using it in case you are pregnant.
If your 100% acetone acrylic remover has methylene chloride in it, then it can be unsafe for both the child and the mother as it is considered a toxic ingredient. There is some remover that has organic solvents in them which might be dangerous to the skin, eyes, a respiratory tract in the bodies of the baby as well as the mother.