Inconsiderate Boyfriend

Kind of a long read, I’m sorry I’m advance! So my boyfriend and I have been together for almost four years, we live together and have one child. For as long as we’ve been living together, he’s had an issue with me going to bars/clubs and being out late. He says that I’m in a relationship and have no business being out that late and places like that. Last night, he went out. I was at work and wasn’t off until 9 pm but he left at 3:30 pm. He hadn’t really communicated much else other than the time he was leaving. So he left, I was going to pick up our son from his parents’ house when I was off. When we talked after I was off, he said they hadn’t left yet and they were just at his friend’s house and were barely leaving to the restaurant they had planned to. He said he wouldn’t be home late. I didn’t start pestering him until 12 am when I hadn’t heard back and didn’t know what time he’d be home. I had called him about 7 times and text him twice but got no response. I thought the worst because recently we had been out together and he got drunk and I caught him dancing with another girl. There’s other things he’s said and done that have really diminished my trust in him so I really thought the worst. I finally hear back and he is audibly drunk at this point and insists he wants to stay out. He ends up getting home after 1 am after being out since 3:30 pm. He confessed to me that several women tried talking to him and he turned them down. One girl complimented him and called him handsome. He said he responded “Thank you, my girlfriend never tells me I’m handsome” and that that was the end of it. To me, that sounds like an opening to continue flirting but he insists nothing happens. I’m just so confused by it all and don’t know what to think and it frustrates me that he doesn’t see an issue with everything. He didn’t communicate from the jump, stayed out way too long after criticizing me of being out for 2-3 hours from time to time, and theres also the very real possibility that he would cheat on me, especially when he’s drunk. How can I get through to him?