I just read through your entire situation. I have a couple of thoughts. These are just my thoughts - keep in mind you should do what works for you.
It sounds like you are giving your H implicit permission to hang out with 'K'. It's one thing to overlook him hanging out with 'K', but it's an entirely different situation to give him outright permission to do it.
Is there any chance you H (or someone else for that matter) would watch the kids at some point where you could do your own thing to GAL? Speaking of GAL'ing, is there anything you could do that would put an extra 'spring' in your step, while getting you out of the house? Think of something maybe "out of the box", something you've always wanted to try. You could even occasionally just take a walk around the block, get some fresh air. You could visit a museum. Go see a movie by yourself. I think IaP suggested going out for coffee with a friend. I think you get the picture.
Another thing dbmod pointed out to me early in my situation - there is a difference between acting "as if" and pretending. When you act "as if", you are acting as if you expect a certain result. There's an example in DR on this.
Hang in there! You're in a good place. We're behind you here and pulling for you.
