It could mean several things. 1. He could be a polygamist and have more than one wife. 2. He could have gotten divorced and the remarried. 3. The woman is a lesbian or bisexual and has a steady girlfriend.
It is simple, your father has married twice, having both the wives at the same time. Yes your father is loyal to both of them as far as they are loyal to him. Second part i.e. mother is concerned both are your mother technically. Your father is loyal to both, because he has married and not keeping any extra marital relationship with any other woman without the knowledge of the first one.