Break up with him.

Your mum can be forgiven, with time and communication. It will be full of ups and downs and there is no promise your relationship with her will ever be the same, but you can try to forgive because she is family. Take all the time you need, it could take days, weeks, years, no one can predict how long it will take for you to forgive, but just take every day as it comes, make sure you communicate your feelings calmly with your mother, because communication is key to overcoming issues like this. And if you can’t forgive her, it will be painful but it is not the end of the world, you will get through it.

Your boyfriend on the other hand absolutely not, imagine if you did forgive him, every single time he interacted with your mother in the future you would be reminded of the events, it could make you paranoid, or send you into toxic behaviours of overthinking. For your own mental health do not stay with him or try and work it out, he does not deserve forgiveness, he cheated and took advantage of a vulnerable moment. There is no excuse for that. Even if he never ever interacted with your mother again, you shouldn’t have to be in the position where you can’t take your SO to see your family, or if you go to family gatherings, birthdays, holidays, you wouldn’t be able to bring him because it would put you in a horrible position. That just seems like an unhealthy position to be in because you would constantly be thinking about how to prevent situations like that, which you shouldn’t have to do.

For your sake leave him. You may love him but love is only 1 part of what makes a healthy relationship, and I’d say you’d be lacking all the other parts (that’s his fault not yours), you deserve happiness and trust, and that is not with this guy.

Btw I hope you’re feeling better from your reaction.

Goodluck.