I need opinions:

My partner and I have been together for two and half years. About two years ago, I told my partner I was going to move across the country for health reasons. He was on and off about whether he wanted to do long distance or not and so this caused us to fight a lot for a few months. He ended up putting his foot down and said he was not going to do long distance so we broke up. Fast forward a few months and I end up not moving because I can’t imagine a life without him. We get back together and he confesses that while we were dating, in the months we were fighting, he told one of his girl friends (who had been a problem in our relationship) that he would sleep with her one night when they were drinking together. They never slept together but who knows why, he claimed he doesn’t remember. I decided to stay because we were giving our relationship a fresh start and he claims he only told her that because he needed emotional love and I wasn’t giving him enough. We have been together for the last two years this summer but it is still something I can’t seem to get over and still have trust issues about. Is it normal to to still have trust issues this long after they cheat?