Is My Girlfriend Cheating on me with my dad?

Okay so here's the situation;

My mother met this girl from a small town who was new to the “big city" so she took her into her home and bonded with her so much so to where she began to call her mom, now a few weeks after they met she disappeared for a full day and as did my dad (but hours later than she did) and when the girl came back she told my mom she met a black dude who was so nice to her and that she slept with him (and my mom believes that she was trying to say she slept with my dad albeit not outright because of her shame) and my dad slowly began to go commando while sleeping more often and one day my mom fell asleep in the tub (for almost the whole day) and when she woke up she was submerged in the water and my dad was completely naked picking her up from the tub and back to there room and that in the guest room where the girl was staying she saw her in panties and a t-shirt now jump forward to Halloween I meet the girl and strike up a friendship and she laughs at my jokes (which are wildly inappropriate) a few months later I asked her to see a movie with me (but with no greater Intention's) and she comes out and say's that she wants to be girlfriend I accept because I think she's cool and we've been dating for two months now and she seems to be completely devoted but shortly after this my Mom told me everything I said above and that she saw deleted conversations with my dad on her phone from recently with the few remaining messages being the following;

“*MY MOM'S NAME* is gone"

“lol"

“She's back nvm"

I would like to be able to continue my relationship with this girl and pretend that I don't think she's sleeping with my dad (who I must add is a very amoral man who will sleep with any woman over the age of 18 so long as their not related to him) but I at least want to know the truth and not be toyed with (like why would she want to begin a relationship with me if she already was pursing an affair with my dad behind my mom's back and why she came on to me first and why she seems to genuinely enjoy our time together)