When I say constant I mean constant.
If you were to mentally or physically map out each hour of the day, each week, when you'd have to be available to answer his contact or do something for him, what might that look like? And what portion of your time do you get to think about you and your kids, and then time for just you?
I did that with my perp and it turned out to be literally 24/7. Even the 4-5 hours I was asleep weren't me time, as he didn't sleep and would wake me up in the middle of the night for sex (and sometimes, didn't wake me). What you said about not being able to go to the supermarket on weekends was exactly the same restriction mine put on me. His reasoning was the weekends were "his" time, and my focus was to be on him, not chores I should have done in the week while he was in work.
It won't help to show him the mapping, he likely knows exactly the demands he's making on your time and attention, and definitely won't feel horrified or remorseful, let alone change. But it may help you get a clearer idea in your mind how unreasonable his behaviour towards you is. And once you have that, hold on to it like your life depends on it.
With regards to your OP, keep in mind if he's broken your trust enough to lie about using a condom, there is every chance he could try something while you're unconscious/asleep (unless you're a really light sleeper, but even then...) if he wants to be extra sure, or suspects you took action like taking the MAP. So if like the other day you think something isn't right, and suspect he tried it again, make a note of it (here would be good, so he can't delete it) and see your gp or the nurse. Maybe consider seeing a different doctor to your usual one, if your doc is also his one.
Again, you're doing really well with the situation you're in, and you're getting some wonderful advice from the lovely people here. Make sure you're keeping your browsing history clear of links to this site or any others linked to help. Consider changing your passwords for e-mail, this site, and online banking, and where possible enable extra login security - but only if you feel it safe to. If he would notice and it would cause problems for you, stick to being discrete and deleting everything as you go along, clear your saved passwords and don't set it to remember them when you next log in. If you use chrome as a browser, log out of Google on it, and disable any synching of history and passwords etc.
Good luck MrsH! And stay safe hugs