The factor you are missing to attach a name here is called 'Ego' in English. It is that ego which is there inside you, and it can get worse in future. There are very few people who can get control over it, and it is through 'self forgiveness' for your own mistakes. If you can do that- you both guys can live together. 

But think practically, if you can not manage the 'ego' factor, you guys should think again. Sorry to say - but from your writing  - It is evident that, you won't be able to 'trust' her in future,.... this ghost of feeling of her sleeping with another guy will be chasing you forever and it has hurt your 'ego'.... and this will create the problem for you guys in future. 

FYI,  there are five stages that ultimately leads to a breakup.

1. Dissatisfaction — one or both partners grow dissatisfied with the relationship.
2. Exposure — both partners mutually become aware of the problems in the relationship.
3. Negotiation — both partners attempt to negotiate a solution to problems.
4. Resolution and transformation — both partners apply the yield of their negotiation.
5. Termination — proposed resolution fails to rectify issues and no further solutions are accepted or applied.

..and you are in between stage 3 and 4. 

I know, these words might sound harsh, but certain facts are bitter and we can not run away or ignore the problem..