Is my father dating my girlfriend?

I am 35 years old and I have dated my girlfriend for five years. We've both met each other's parents.  

However, she frequents my home and my father always gives her money whenever she comes.

One time I found her home talking on phone, she told me that, her brother needed her help urgently. I gave her transport money and she left.

However, I followed her on a boda boda and to my surprise she had gone to meet my Dad who hugged her as soon as they met at a certain bar. They sat and he ordered for beers, I decided to leave because I couldn't handle it any more.

I've since wanted to confront either of them but how do I do it without sounding disrespectful to my father?

Henry