It sounds to me like the big issue is with your partner. That other woman seems to have just been caught up in it. If he is that apathetic about the relationsship that he doesn't care if he has your trust or not, then that sounds like the crux of it all.
I think you should find out if he is really apathetic. Does he really want to continue the relationship? Maybe it would be good to allow the relationship to grow apart as opposed to try to stick something out that could cause resentment.
You sound very reasonable in dealing with this. It would be very easy to forgive and try to forget or work past this. However, I think that this is a huge warning sign that needs to be addressed instead of dealing with the symptoms of the cheating.
i wish you well in dealing with this.