HiCustomer Thank you for asking your question on JustAnswer.
It sounds like your father may be going through a midlife crisis and has left everything for someone that makes him feel younger depending on his age men typically go through midlife crisis around the ages of 39-50 and usually it happens over a period of time where they are feeling old and unattractive. Some of the sign that you father may be going through this could be that he no longer knows who he is or what he wants, somewhere along the line he lost connection with who he was. He may have felt lost like he didn't know what he wanted out of life. He may have been feeling some regrets about not doing things he wanted to do because he had a family to take care of all of these years. He probably likes the attention he got from this other woman and the way she made him feel young and vibrant again. He may be thinking that his time is running out and that he wants to feel young and alive.
The things that used to make him happy now cause depression, wanting to experience new things, leaving a long term relationship or marriage. These are all sign that he is going through a crisis and it may be a phase but you cannot really be sure how long this phase is going to last. What you will have to do is show him that no matter what he is still your father and that you love him. What he is going to have to do is either get some counseling for his issues and maybe talk to his Doctor about his midlife crisis. You cannot make him come home if he isn't ready to do so. He is going to have to see that this isn't going to last forever and what he gave up is so much more important than feeling loved by a younger woman, he may be having fun now but it gets old quick and he will realize that he cannot handle the type of life this young woman has.
He is going to have to realize on his own what all he is giving up just to feel young but you have to know that you are not alone many families go through this same thing where the husband leaves them for a young more adventurous woman and then they realize what they gave up and want it back so let's hope this is the case with your father but don't allow your mother to wait all the rest of her life for him to decide he wants to come back.