Hi Shazzy and welcome to SR.
First things first, you can't do anything about whether someone chooses to drink. I'm assuming your partner is an alcoholic. His choice will always be to drink. Its not personal. It feels personal, it feels that he just doesn't care, it feels that it doesn't bother him that you are crying your eyes out. That is kind of true and not. Alcoholism drives a life "My partner chooses to drink over anything else in the world" is the definition of being one. While he may wish that you weren't so upset he cannot stop. He will always choose alcohol over you, your children, friends, family, jobs, or anything else that a person who is not alcoholic would put first. You did not cause this, you can't control it and you cannot cure it. The 3 c's that you need to learn.
What to do - First you need to put your children's needs above the needs of the alcoholic. Children who are raised in alcoholic homes suffer terribly. The alcoholic does not have to be abusive for that to happen. What happens is the entire household centers around the alcoholic and their needs - such as your children are exhausted today instead of getting a good night's sleep because the A's friends and drinking were priority last night.
What you need to do is work on you and your kids and not focus on your partner. I'm not telling you to break it off, I'm saying that you need a priority shift. You need to learn about codependency and enabling and how it is the foundation for most alcoholics to function. Start by reading here about codependency. I also suggest (strongly) that you start attending Al-Anon.
"He's out having a great time and I am left at home bawling my eyes out". I am sorry you are hurting. Alcoholism is not fun. Addiction is a horrific way to live. If you could crawl inside his mind you may be surprised to find out that he isn't having much fun at all - rather is chasing the bear. Addicts are always trying to get back to a place where they were pre-addiction, and drinking was social and really was fun. Once it crosses the line it is a miserable job. As you are not one you will say to yourself "well he should just quit"!, but he can't. He could choose to seek recovery from his alcoholism but he is not in that mind frame. Alcoholism is a disease of denial which perpetuates it.
I hope you stay on here and post often we are here to help Lots of (((hugs))) sorry you are going through this but there are things you can do for yourself and your kids that will make life much better.