hi there
Firstly, I'm so sorry you are going through this

It stinks and I went through similar stuff wayyyy back. I'm 30 now (ancient) but I remember how hard it was so I wanted to stop by and chat.
Before I discuss ANYthing - I want you to know that it is
NOT appropriate for your mother to be hitting you. While some parents do believe in spanking; hitting is very much different. If your mother is literally hitting you, that is not an appropriate reaction at all. Parents seem to do this sometimes out of anger - and that anger most often comes from situations that aren't related to you. Please know that you do NOT deserve to be hit. Nothing you could do as a young person would ever truly necessitate being hit. That responsibility lies outside of you so don't blame yourself.
I also want to tell you that in adult relationships, cheating does occur - and it occurs for a wide variety of reasons. None of those are ever related to kids either. Sometimes Mom and Dad have just grown apart. Sometimes they don't have the skills they need to work their issues out, and so they seek people outside the relationship. Sometimes they are lonely because they are fighting with each other, and they seek attention from others. Humans need attention - it's a normal, valid thing to seek, but the type of attention your mother is getting is not appropriate. As a mother, she should be reaching out for attention in ways that are healthy - such as hanging out with her friends, seeing a therapist, or doing a hobby with others that makes her feel good.
While I agree that what your mother is doing is very selfish, it's important that you don't blame any of the whole situation on yourself at any point

Adult relationship issues are never the responsibility of a child - it's not your job to fix their relationship and you shouldn't feel responsible for doing so. (Maybe you don't but I thought I'd throw that out there).
Are you in the United States?
I want to give you some places you can call. Before you call, make sure you are safe. If you think calling would upset your mom or dad, then call when they are out or call from another location.
If you are in the USA, you can call and speak to a friendly counselor at ChildHelp. There number is 1-800-422-4453. It's anonymous! You can talk about as little, or as much as you want - and it's not going to result in someone calling your mom unless YOU decide you want to connect on a more local basis. These guys are excellent

Great to just chat to about what is going on and they don't judge
If you are in Canada, you can call The Kids Help Phone. Their number is 1 800 668 6868. You may be able to reach that number from the USA too - I'm not fully sure.
The most important thing for you right now is that you have someone to talk to, in addition to us here at PsychCentral :0)
You sound like you really need someone in your corner right now. Is there anyone in your life that you would trust? A doctor, an adult friend, a teacher - a counselor, priest, nurse - any of these people would be a great choice

And they will all be accepting of your contact. They are community leaders - and most community leaders can help you to sort out some of these thoughts.
I'll keep an eye on your thread to see if I can help further :0)
Please be kind to yourself right now - this a lot for any adult to deal with let alone on top of being 13.