Should i have given him a second chance?

My boyfriend and I started dating about a year ago. Within a month we were in a committed relationship and officially boyfriend and girlfriend. There was a distance issue I will admit. I lived an hour away from him, but I was the one who was always willing to go over and see him. We made it work or at least I thought so. He had a rule that he introduces his gfs to his family only after six months. Well six months came and went and there was no mention of meeting his parents that lived in the same town as him. Also there were many times that he would cancel on our dates because of some reason or another and when we did hangout we would just stay at his home and order in. I was okay with this arrangement because I said he felt like a homebody and on his spare time he just liked to stay home. There would also be certain days that I couldn't go over because he worked early the next day.
Recently, I was away for work for almost a month and when I got back I started to notice things at his house, a new toothbrush in a different drawer, some makeup stuff and a note on his bulletin board that said, "****, I kinda like you. - CA" I tried to give him the benefit of the doubt, he told me that he has some "girl" friends and lesbian friends that these could have been from. He even said he hung out with his lesbian friends and that I shouldn't worry because they don't like men...
When I finally had a strong feeling that something was going on, I drove to his house one night and saw that there was a different car there all night. That was the final straw and I was planning on confronting him that next Sunday afternoon. But then on the Saturday night before I was going to see him, I found the girl's Instagram with him all over it and her saying this is my new boyfriend. All the pictures started when I was away on my work trip.
I confronted him the next day about this "girlfriend" and he said she was just a friend that he hung out with sometimes. He admitted to me that she knew about me but told her that I was only a 'friend'. That he was lonely when I was away and they started hanging out and messed around a few times. I had grown to love him during this year and it was hard to accept that he could do this to me, but all the signs were there. I asked him how long would this had gone on if I didn't find out about it. He answered saying until I decided which one I liked better. He said that he like us both for different reasons and that he kind of just wanted both of us. I asked him to choose and he was unable to at the moment and had to think about it. I was not okay with this, with him being with another woman at the same time as me. I felt so dirty. She was in the same bed that I was in. I asked him if he wanted his key back, but he said to hold on to it until he had time to think. I left to a friend's house but then decided to drove back to give him the key back. I felt that if I still had the key, I would have hope that he might pick me. That he might want to stay with him and dump her. But then I thought that if he didn't pick me, I would still have to come all the way over here and give him the key back and if that was his decision I didn't want to face him again. So I gave it back and ended our year long relationship on my own terms. In essence, I made the decision for him. Currently he is still with the other girl, who is almost 10 years his junior. This is a 35 yr old man dating a 26 yr old.... gross
I decided to message her on FB to warn her about how he is. That he was an excellent liar and was not only cheating on me, but on her too. She didn't want to listen and said she felt bad that I felt he led me on. She had met the parents or knew them before they started being together, and that she hung out with his friends. She said I was the liar and that she trusted him completely. I didn't feel mad, but I felt pity for her, that she is so young and naïve that she would believe all his ****. I also felt hurt that he could dismiss or relationship so easy after telling me he couldn't imagine me not in his life, just hours before.
I didn't want to play all her games so I didn't respond, and blocked her. I am a grown-ass woman and could not tolerate my boyfriend cheating on me. I have more self-respect than that.

I want to say once a cheater always a cheater, but in a small way, maybe the part of me that still loves him. I wondered if I should have given him the chance to prove he wanted me and not her. That I should have held on to the key and made him make the decision.

So the question I pose is this, did I react too quickly to break the relationship or should I have given him a second chance and let us work on the relationship? Yes, it was only a year together and we did have kids or anything to complicate things, but there was love and there were good times too. He valued my intelligence and we had good chemistry and liked all the same things. Could I have gotten over the fact that he cheated on me? Is it that easy for women to forgive their boyfriend/husband? What are these modern girls/women thinking when they know their boyfriend/husband is cheating and how can they be okay with that? All I know is that I wasn't okay with it...