I am married and I have a gut feeling my husband is cheating on me

I have been married for almost 12 years. My husband wanted to have a vasectomy after I had our 3rd child.

He insisted that he should have the surgery because it was easier on a man. I have constantly been accused of cheating on him for the last nine years and he keeps telling me that he would never do anything to hurt me or the children.

I have a gut feeling that he has cheated on me in the past and I feel like he is seeing someone now.

What do I do?