Is enthalpy the same thing as potential energy?
In any way, ignoring the definitions given in a textbook is a bad idea. As for the question, the main problem in your thoughts is that you mixed too many things from different fields of science. Your example (two particles, kinetic energy, potential energy etc) looks like classical mechanics. So if you want to explain it, please, use tools offered by classical mechanics. Enthalpy is a measure of total energy in thermodynamics. It is used to explain processes taking place in large systems, which can be characterized with volume, pressure, temperature etc. It is not used to describe one particle. 
Maybe you can take it into account and revise your question. Make it clear exactly what you want to understand: change in the kinetic and potential energy in interactions of two particles or change in enthalpy in exothermic and endothermic reactions.