One thing you need to understand is in her current mindset, everything is your fault and you can do nothing right and everything wrong. I'm sorry to say it's only going to continue getting worse from here. My suggestion would be that since you're both under the same roof and effectively are in an IHS then you come up with a schedule for watching S. You agree to be home certain evenings by a certain time so she can go do stuff and vice versa, she agrees to be home certain nights so you can do what you want.
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She needs me so much and talks about walking on our marriage vows?
I think you're getting confused, she doesn't "need" you as a husband, just as someone to do errands, watch the kids and take care of other beta stuff.
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If she challenges me about this weekend’s dinner, I’ll say “I’m sorry you feel that way. I was really looking forward to having dinner with you then, as I made reservations. If you don’t want to go, you don’t have to, but that means you can put the boys to bed as I’ll just go out, and you can join me if you want.”
Just tell her you're going to cancel the plans and then cancel them. Say nothing more about it. Don't pine away about how much you wanted to go with her (pursuit). Learn to be VERY brief with her.
Fair enough. I should remember that she doesn’t really ‘need’ me as a husband—rather, I’m a glorified roommate, and act accordingly.
Also fair. If she asks or complains, I’ll just say ‘okay, I’ll cancel the reservations.’ Boom, be done.