Is it me?

My boyfriend and I have been together for a year. We had both gotten out of long term relationships prior, and each spent about 6 months being single. His ex has caused a lot of problems, popping up at his house to “drop off hats” emailing him as a last attempt for contact after he blocked her. Well I got a message from her friend in September saying he told her we weren’t together and they hung out. I brushed it off, because they wouldn’t send me screenshots or anything of that nature. There wasn’t proof, and he was with me every day. Then I started seeing her name in his Snapchat, and he insisted it was a girl from work that works a different shift. I don’t come off like I am accusing him of anything when I approach him, I just ask. It always turns into how I am crazy and blah blah blah. He can be so manipulative and controlling. He literally counts to three at me when I get upset. Anytime I try talking to him about how I feel, or concerns I have, he shuts me down. I guess I just want advice on if I should leave this relationship or not. I am 25 with two kids, and he throws them in my face about how I am lucky to have found him because he accepts them. It’s just hard in the situation trying to establish if this is emotional abuse or if I have no right to be upset. Please help!