You are in a challenging position, and I’m sorry there’s no simple solution. I don’t know why you were looking in your dad’s phone, but you should stay away from it. Here’s what I’m thinking...
If your mom is disabled and can’t earn an income without your dad, what’s she going to do? If your dad treats her well (apart from cheating on her), she’s probably happy how things are. And if your dad doesn’t mistreat you, I’m not sure there’s anything to be gained from telling her.
I want you to try and get your head around this, without messing with your sense of ‘right’ and ‘wrong’ because you obviously have a moral backbone and that’s good. But life is complicated so here’s what I want you to think about.
Your dad may still love your mother. But maybe she’s not meeting his emotional or physical needs, and so he’s cheating on her. But he hasn’t left her. Perhaps he’s just coping the best way he can.
Your mother might already know your dad’s cheating. You figured it out, so there’s every likelihood she has as well. But it would probably break her heart if she knew that you knew.
You’re the child. They’re the adults. They are probably both trying to protect you from harsh realities and keep life ‘normal’ so you can go to school and grow up without any more drama than is necessary.
If you confront your mother or your father you will completely change the dynamic within your home. If you bring his cheating out into the open air, your parents will have no way to continue the way they are now.
Should you ‘protect’ your father? No. Should you tell your mother? No. Should you touch your father’s phone? Never!
I believe you should be concentrating on studying and having fun with your friends as well as being an active, helpful member of your family. Don’t get involved in the dynamics of your parents’ relationship. Just concentrate on staying out of trouble, so things don’t get any more difficult than they already are.
I understand that you don’t trust your dad, but if he’s doing his best to support you and your mom, you have to give him some credit for that mentally. We don’t know what the future holds but you should not lose sight of the good parts of how life is in the ‘now.’