It's perfectly normal (and healthy) to feel sadness, hurt, anger, shame, and frustration over this situation with your father. While it may be tempting to ignore your emotions and just move forward, it's not a prudent thing to do. If you don't deal with your feelings today, they can resurface later in life especially in relationships with men. Stuffing them can lead to a lack of awareness followed by destructive patterns. It's best to process all your anguish now in a deliberate and conscious way. I urge you to do this with a therapist.
Tell your mother that you'd like to talk with a professional. She's struggling with her own feelings, having picked this man in the first place and then letting him back into your lives. She may be experiencing guilt for her bad choices and, therefore, can't be receptive to your emotions. She may want everyone to move forward, pretending damage hasn't been done.
As fatherless daughters, we must realize that our moms may be ill-equipped to hear our pain and empathize with our feelings. When I was a girl, I tried to talk with my mom time and time again about my dad, but she'd always shut me down. That's why a therapist, an objective person who won't get defensive, can be so helpful.
Like other fatherless daughters, I didn't deal with my dad's rejection until I reached a breaking point. When I was in my 40's, my son was diagnosed with autism and everything fell apart. I was consumed by anger, hate, and resentment and became blind to any beauty in the world.
It took a good therapist to help me see that my rage had nothing to do with my son getting diagnosed. It was simply the event that triggered it. Rather, my anger had to do with the unresolved feelings I had about my dad's absence. Sarah Fields said, “Hate is just a bodyguard for grief” and that was certainly true in my case. I had to let myself become vulnerable and get in touch with the profound sadness I'd felt like a girl.
After acknowledging the hurt I felt as a child, I was finally able to move forward. I became very intentional about my healing by spending time in nature, eating consciously (I became a vegan), and developing daily spiritual practices such as meditating, praying, and writing in my journal. I used the mantra “you can't heal what you don't feel” to remind myself to stay on top of my emotions rather than bottling them up.
I once thought being strong meant not dealing with your feelings. Now I know the opposite is true. I wish you the best!