Need some Christian Advice...please.?

I was raised Christian and my dad was a pastor. After he died when I was 14, I faded from church and God for awhile. Not that I did not believe in God anymore, but I just felt lost because my dad kept me strong. 3 yrs. after I ended up meeting a guy my senior year of high school. And I thought he was the one I can spend the rest of my life with..but he is Catholic. He is strong on his Catholic beliefs and does not want to convert. His parents say I am suppose to convert because I am the female. But I convinced him that our religion should not define our love. After being together for 5 years, I found out that he cheated on me, we took a 3 month break and I forgave. My dad always told me and my sisters that our 1st boyfriend should be our last. So I tried to stick with that. Then 7 months later we got married and 3 months after that I got pregnant. Unfortunately, I lost the baby due to a tubal pregnancy but the doctor asked me if there was someone else, and she apologized because she did not know how long we been married but that her testing definitely revealed that there is some one else and that it was recent. At the time I was so out it and in a lot of pain, but I wanted to question my husband. But that same day he found out a close cousin of his died so he had to go out of state for his funeral. I never got a chance to confront him at that time. And when he came back I forgot about it. But from time to time it would come up with the help of my suspicions of him messing with other girls when he goes out to drink with his brothers because his stories do never added up. I also heard he tried to cheat on me with 2 of my friends when I was out of state. I finally confronted him about everything but he said he has never cheated on me beside the 1st time before we got married. But for some reason I have this feeling that he is lying. I asked him about what the doctor said and he said he doesn't know what she is talking about, and its probably a mistake. I keep letting things go because I do not like to go off of hearsay and I really dislike arguing. But from time to time it comes up in my head and it upsets me. I keep praying and asking God to please advise me on what I should do. Sometimes I feel like God is saying to work things out & sometimes I feel he wants me to leave. But then I know divorce is not right. I am so confused...I know my husband loves me, and he is trying to go to change. But I also do not want him to change just for me, because it makes me feel like I am forcing him to change. He smokes & drinks too. Should I just keep praying for our marriage to work? I complained about him drinking and smoking. And he said he will stop but he hasn't, but he has cut down. I am also worried about when we have kids. I do not want them confused about which religion to follow. I have been trying to be more humble and forgiving and get back into church and living by the word. But its hard because he is so much of the world. He sits with me while I pray, but I guess I just want him to really try harder to quit his bad habits. He also plays violent video games and it increases his profanity. I know I am not perfect, but what do I do? Are there other Christians going through this? His whole family drinks and smoke so I think it will be hard for him to quit. Is it wrong to get a divorce because I do not feel equally yoked with him? Do I just stay married and hope it will get better? If you are Christian your advice is appreciated. Thank you