First you need to find out what kind of paint he used. All paints are either oil based or water based. Most spray paints are oil based, but someone told me there are water based spray paints also. If it is water based, then it should wash right off with soapy cold water. (The original paint is definitely oil paint, so the water won't affect it.)
If it is oil based paint, and it probably is, you will need to take it off with some type of hydrocarbon. Your dad might have some paint thinner around the house, since he also had the paint. Your mother's nail polish remover will probably work and so will. kerosene. Take a clean cotton cloth and wet it just with one fingertip. Then try it first on some small spot on the underside of the bike where it won't be noticed. Experiment with it a little bit. If it does remove too much of the original paint on that little spot, then don't use it on the spray paint. Try one of the other things. Do just a small spot at a time and then wipe that spot clean as soon as it's finished so that it can't keep on working on the original paint. (Also, make VERY certain that nobody is smoking anywhere near you when you use these things, they can catch fire or even explode.)