I’m sure this is really hard for you and for your brother. Your mother is evidently going through some issues of her own that have negative consequences for both of you. I’m guessing you are feeling abandoned and your brother is confused about whether he is supposed to step in as a “parent” since mom isn’t doing the job.
Your mother’s private life is exactly that — private. You had no business going into her phone. You have no business telling boyfriend A about boyfriend B. She’s obviously feeling defensive about her decisions or she wouldn’t react to things you say with shouts and physical violence. That certainly isn’t acceptable.
Leaving your alone for hours and nights at a time means she isn’t doing her job as a mom. You and your brother do have legitimate complaints about how much of your mom’s time and attention you are getting. You don’t deserve to be hit, ever. But the way to handle this is not to violate boundaries even more by spying on your mother or by sharing information you aren’t supposed to have.
I don’t think it is wise for you and your brother to hold onto information that makes you both so uncomfortable. But it’s important that you not judge your mom for information you got by grabbing her phone.
Instead, think about whether you and your brother can calmly sit down with your mother and tell her that you know she is trying to figure out relationships but that you miss her and that you miss having a family life. Don’t “confront” her with her dating behavior. Just let her know that her absences at night worry you.
Approach her with compassion and stick to what you need from her that you aren’t getting. If she gets upset, don’t get angry in return. Adding angry noise to angry noise only ups the noise. Sit quietly and repeat that you aren’t judging her but that you love her and miss her and that you worry about her. See if you can work out having time with her. Tell her that, at 13, you still need a mom. It’s not your brother’s job to be your “parent”. It’s not your job to try to parent yourself.
If your mom seems to want to find a solution but the three of you can’t figure it out, see if she would be willing to see a family therapist for a few sessions to help all of you. Another option is to ask to live more of the time with your dad while she figures out her life.
I hope your mother is able to respond to you. You clearly care about her or you wouldn’t be looking for a solution.
I wish you well.