She has to earn your trust. Two red flags - 1/ she is blaming you for her actions, 2/ only you're are seeking counseling instead of having couple's therapy.
Regardless of whether or not she was cheating with one or multiple partners, you did not cause her behavior. She made a choice and even now is denying responsibilities. If she does not seek to improve herself and the marriage, you are going to live in constant doubt of her fidelity.
I have talked to her about going to counciling with me. However, she thinks that the only reason I want her to go is for her alcohol abuse.