You dont need our permission to feel a certain way or take action but you should do and feel what is best for you. Only you can decide whether trust can be rebuilt or not. For me the answer was no when my AEXBF relapsed but denied. But thats based on the type of person i am - once trust has gone no matter how much someone tries i never fully trust that person again. Therapy helped so me that i dont have to stay in a relationship for any other reason than i want to & im happy so that allowed me to end mine before things got too bad, still heartbroken but getting better everyday.
Good luck but please remember you are important too & so is your happiness.