Newly wed (honeymoon phase expired)

So I have only been married two months and  my husband is currently living in a different city because of our jobs. We have two kids together and we've been together since December 2011. Everything was fine for a LONG time but when he came to visit recently I found out that he was texting another woman about going to see her. When I confronted him he said it was a moment of weakness, and he apologized for it. He said he isn't used to being away from me and it has been very difficult and he isn't used to it. I asked is this the only incident and how long. He said this was the only incident and once he realized what he was doing he stopped texting her. I'm upset because we've only been married for two months and I just feel like it was too easy for him to fall into temptation, we haven't had something like this happen since 2012, I thought it was behind us. Now I am questioning EVERYTHING. I don't want to live a lie, I don't want to be married to someone who isn't loyal. On our wedding day his vows were everything! Now I am even questioning those very words! We have since then talked about it, and I want to believe everything he is saying and forgive him, he even cried in my arms (he never cry) but I am still shocked that this is actually happening. I know marriage isn't all peaches and cream but this isn't the type of problems I was expecting.  Any advise would definitely help. I've prayed about it and talked to him but I'm still hurt right now.