Defective Neutral Safety Switch causing shifting problems?

What is your question?

My car behaves normally when cold. After it has warmed up, if it is shifted out of drive and then back, it will not engage. Also it will not hold reverse when it is warm, but will when cold. When I got the car, it backed itself onto my trailer for the trip home with no trouble. I never have problems starting the car, and it will only start in park or neutral. Could this be the neutral safety switch or is it an internal problem? I am not getting any diagnostic codes, and the MIL never comes on when the problem happens.