How I was raised and how my mind works. Getting a divorce is failing to me.
I think this failure needs to be placed on the shoulders of the person who broke the trust.
I agree with this. Divorce felt like failing to me, but through lots of counseling, I realized that I was not the one who failed and I had no control over his shortcomings. Ex was the one who failed by cheating when things got tough in our lives instead of confiding in me as his spouse and partner. I set up the counseling when I found out he was a cheater and a liar. I was willing to put in the work. He wasn't. It was "too hard" according to him. That's his failure, not mine.
Similarly, you did not choose to put a profile on a gay hook-up site. Your h did. If he really wanted to explore that side of his sexuality, he should have talked with you - his wife and partner -- about it. How is that your failure?