How do I test a previously painted pool to find out whether it can be repainted with epoxy?

Simply rub the existing surface with Acetone solvent, or Colormaker CRS on a clean rag. If the paint softens and becomes sticky, it cannot be painted over with epoxy, but probably can be coated with Chlorinated Rubber. If the solvent merely removes some surface oxides and does not soften the paint, you may use epoxy. Test the pool surface in a number of areas so as to ensure all layers are the same.