he thinks im cheating

so we have been dating for almost 2 years. we got pregnant about 4 months in. tbh I love him, but he has a terrible drinking problem and anger issues. he is manipulative too. I wouldn't try so hard to make it work if we didn't have a child together. half the pregnancy he didn't have a job. he has one, but barely goes. he never helps with expenses. we don't live together. he cheated on me 3 months after our child was born (I had post partum depression and was withdrawn from him). I still struggle to trust him, I have never cheated. he keeps saying that I don't want him so he thinks im cheating. I go to school and work fulltime and my baby has a schedule. it's hard to find time to have sex. and I don't want to if he's an ass all the time. he doesn't understand.