That sounds hard FS. I'd be really really angry in your position too. It's a lack of respect, isn't it? An assumption on his part that you are the default parent. What would happen if you refused to take care of the children on his work days? He'll never need to find out because you wouldn't do that - and the way he does the childcare schedule sort of demonstrates he has that kind of confidence in you. It is a hard place to be because you have very little choice. I have a lot of resentment like this too - thinking that if I'd done what H has done - picking and choosing when to see his kids, seeing them in my house for a couple of hours twice a week, doing no significant childcare at all - then he'd be absolutely scuppered. And he's never needed to worry about that, the way I've had to worry about whether he will take them when I'm away next week, and cope with it, and parent them both properly. It is hard.
Do your friends who think he is scheming know you both well?