P.M.
Standard commercial nail polish and remover are NOT SAFE. They contain several highly toxic ingredients, poisonous to the liver and other organs. Both the fumes and the liquid chemical get into those little bodies by the lungs and directly through the nails, which are porous. Small children with developing bodies and brains are much more susceptible to toxins than adults.
There are specially formulated polishes for kids that are safer. They tend to peel off easily, but this would make it unnecessary to use a toxic remover.