No matter what, the fact that your partner was with someone else is going to be a huge issue to deal with in the relationship.
The fact that she has no memory of it (if you believe that to be the truth and can tell that she is telling the truth) then, I would say it's hard then to say she was cheating. It would have been a part of her that is very different from the one that loves you.
That still does not take away your pain, the need to address the situation, therapy for the two of you would be a good thing I believe, and if she wants to make this relationship work she needs to figure out what is going on with the other parts of herself.
Although, I do know that for some with DID that is harder than for others.
I really think you are in a better position to judge this one than we are honey.
We can offer you are advice, support, care, and we can be here for you through everything that happens because we care so much about you.
But you are really the one that knows her and your own heart and relationship the best.
*Cuddles and lots of hugs*
It can't be easy. Let us know what happens and what you decide and how you are okay? I am concerned about you. I want you to be safe and to take care of yourself. Please don't feel like you have to be alone in this.
If you need to PM me or someone here you are close to, or post more, do something relaxing for yourself, take it easy, and give yourself some time to sort it out.
Hang on.