I have always used baby oil or skin so soft from avon and it really worked.
Take a cotton ball and moisten with baby oil or the skin so soft and the face should wipe clean!
For the hair, I sprayed down the gummy part of my daughter's hair real well with skin so soft and combed it out little by little to get the tangles and gum out then swept through it again with a fine tooth comb and got all the gum out!
Rather than using peanut butter -I tried this and it worked better.
Removing Gum from Hair With Skin So Soft
When little ones insist on learning to blow bubbles with bubble gum, a parent will eventually have the inevitable chore of gum in someone's hair. LOL It is even more exciting when the hair is on the head of the seven week old newborn, with masses of it. Her older brother did not make a bubble on the first attempt, in fact the whole piece became the glob of gum that stuck to his sister's hair.
Mom, knows better then to use peanut butter, the oil just can't cut the gum, or ice, what on a baby? Skin so Soft from Avon is the most amazing degummer in a pinch. Gum always seems to get stuck at the most inconvenient times, and Mom always carries a small little bottle in her purse for those greatest needs. It smells better then PB, it is washable and not so greasy and Gumout is too toxic for the little ones.