I would set her up with a therapist, lay it out for her during the first session with the therapist's guidance, and then kick off individual therapy for her from there. If you can't afford it there are usually programs through the school for children. I was in a vaguely comparable situation in middle school and they gave me a social worker for a few months during lunches at school. It helped. There are also free support groups like al-anon, and even al-ateen which is specifically for people in exactly your daughter's situation. I used these resources as a teenager and they were immensely, immensely helpful. There are plenty of self-help books and online forums available now that weren't around when I was going through this so I don't know many unfortunately but I know they are out there.

Either way, putting knowledge and understanding in her hands are the best ways to empower her to navigate through this. Make sure she has a strong emotional support system and then when she's ready she can take the reigns in the relationship with her dad.

Right at the beginning though, there is bound to be tumult. She is becoming an adult and is not naive. As you mention, she is already very suspicious and has now been rejected on her birthday and no one will tell her why. She is going to be putting a lot of things together, pieces will be falling into place and she will feel lied to and hurt and confused. It would be best for you both to pre-emptively involve a professional with experience.

You can't hold out on her much longer, though. If she puts this together on her own it could cause a real rift between all three of you.