It is understandable that you are struggling with trust. Anyone would in this situation. Once a partner cheats everything in that relationship changes. Things that would not have caused turmoil takes on a different meaning. You have the benefit of your partner's oath that he really does want this relationship. If he is serious than he should do whatever he can to make it right. When his travels have ended think about a couples counselor so the relationship can be built on a strong foundation. Do everything you can to have positive communication whether that is couples workshops or self help work - the best communication guide is Mars and Venus Together Forever which includes the rules of fair fighting.
When he returns you have to be brutally honest about your fears. Develop a plan that will mend this. Negotiate. Establish boundaries that he isn't to cross - whether that is that you only go to these outings together. You have to establish these as a couple. Come together like someone would in a business deal. This too is a partnership. If you are to succeed with this mistake then you have to come together like you never have.
With all of these remedies you will have a relationship based on communication. If he sincere he will do all of these things and do them willingly. Talk when you are feeling insecure and ask for reassurance.
If this has been helpful press accept