I am sorry that your kids are around this. The good thing (although it might not seem like it) is that J wants them in his life. That is important. So many children are just cast aside by the MLCers, and that is hurtful too.
A smart dog, and you are handling it well. As for OW what can I say. It boils down to the simple truth - what kind of person sleeps with a married man? Even my crazy xh admits that I was right about OW1. Frankly you did not have to be a genius to see that one!
WH you have weathered the most awful period and your courage and grace are amazing. Your husband was a fool to leave you and an even bigger fool for not realising it!!