I'm sure I will get rail roaded here but here it goes anyway...
KECH - first off your H's A is not appropriate but it is a sign that your M is broken. The A is a symptom not the problem.
Second - you can eye roll all you want to the line of "if you loved me like I wanted" all you want. Maybe its true, maybe its not... BUT - IT IS HOW YOUR H FEELS. So its his truth. Whatever happened in your M your H has felt pushed aside with his needs NOT being met as how he needed them. This happen so much in M because communication gets lost especially when life spins in with jobs/kids/etc. You need to understand its not an accusation but an honest line of his feelings.
Third - I totally feel that the line at the Dr office was his way of acknowledging your feelings. I think he has been seeing enough "positive" things that got him thinking about his role in all this and his choices. But, rather than you simply stating that it was something you had hoped for or how the kids will benefit from him being home more you snapped at him. Sending him to vividly back to the woman he chose to leave.
Yes - they get angry. They get angry because the start to see the person that they loved and they needed. You are capable of being the support system they needed and desired... so why weren't you all along???
I can't tell you how angry my H was with me. He point blank said "I could have been this way all along but I chose not to... my choosing not to was a direct slap in his face... and now that I am he is more confused than ever... he doesn't know what to believe." This anger/confusion stage can take awhile for them to sort through.
I can tel you my best male friend gave me that exact perspective when he finally walked out of his trouble M. He said it took him a long time to get over his anger about her ability to make more effort now that he was gone rather than in all the months he stayed and begged for things to be different.
I am also of the working theory that A's happen because a spouse is seriously lacking in have needs met in the M. Yes of course there are serial cheaters out there because they can't do monogamy but most A's happen because some connection isn't being met by their partner. That doesn't make it right but I treat it as a symptom and not the reason.
Stop pouring gasoline.
Give yourself a time out. You've made your statements to your H 1) he feels your resentment for choosing not to travel after he has left, and 2) you do'n't believe him in regards to the A.
Now, stop engaging with additional texts. Take some time to focus on what your H's truth is - what did he mean by his words, love me like I wanted? I show my H I love him by keeping a clean house and doing all his laundry... I do those things because I love him but he doesn't feel my love by things that I do... he needs physical touch - hand holding, shoulder massage, hugs, etc. In the past how did you and your H communicate love? What is your H's love language? Have you ever read The Five Love Languages?
I'm not discrediting anybody's advice because non of us are experts here but I feel you would be foolish not to investigate your H's feelings from his statement.