My therapist is trying not to dig into my past too much, because he says it can exhaust me. So we mainly talk about things on the surface but his attitude irritates me because without digging in, these problems keep existing. Should I tell him that I'm ready to do it?
My mother used to chase me around the house for no reason when I was around 4 and would catch me and touch me and I kept saying no, but she never stopped. This lasted for years.
My father said to me 'you make me horny' when we were taking a bath together when I was 11, and this is the first time I saw an erected penis. I just ran off. I told this to my mother about 10 years later and she said 'that was your fault'.
Were these abuse?
You can let your therapist know that you feel you need to dig in your past for some answers to why you feel as you do now (just the examples you gave are good enough reason to do so). If he won't do that, you might need to change therapists. Every therapist has a different approach and it is a matter of finding the one that works for you.
The incidents you described with your mother and father were definitely abuse. Your mother did not respect your boundaries and did not listen to your feelings. And to keep doing that to you for years against your will says that it was abuse.
And what your father did was sexual abuse. A father should never bathe with a female child and certainly should never expose himself and tell his own daughter she turns him on. It is abuse and it is traumatizing to a child to experience what you did. This sounds like the source of your feelings about men in your current relationships.