How to resolve this issue about another girl when he won't talk? I need this to move on with our relationship?

I think you should dump him.You don't trust him because you know deep down he is not trustworthy but you want him to tell you things you want to hear to make things better but you know who he is and he will only end up cheating on you in the long run.Any guy willing to cheat on you and disrespect and betray you like that does not love you.That's not love and like you said your gut tells you he would have cheated had she not rejected him.You probably fear being alone and not finding better guy out there so your holding on to this loser that clearly does not even care about fixing things.This is your insecurity talking and it's not true.You are so much better and deserve better so you WILL find better.there's plenty of fish in the sea trust me!Take advantage of his fu%& ups and ask for a "break"..you will see how many guys are out there for you!