First -- bravo to you for working to make some real changes for the kids. You will not have to micromanage them forever, but yes, you will have to do a full-court press here, especially for the middle schooler, because MS is when kids simply have to learn to study and turn in assignments, so they are not overwhelmed and failing in HS.
Becoming organized, setting priorities and making choices about which homework should be done first, or which can be put off, etc., are all learned processes; children are not born knowing how to set priorities, or how to study effectively (or at all), or how to budget their time.That's why, since your kids need to learn those basics, the "let them fail and take the consequences" idea -- while it IS a good one at times -- isn't the one for them, not yet. You know that doesn't work with your kids right now anyway.
You can do this and you're determined. But it could mean making some time or shifting the kids' schedules in some way that you and/or dad can get short but very focused face to face time daily, even in the evenings, to review what they are doing. I don't mean "review" as in "check it's correct." Not your job. Instead, look at what tasks they have, talk through priorities and ensure they have what they need. "Read me what you've been assigned for the week.....OK, so the English one-page essay is due on Friday and the math is due on Wednesday. Today's Monday. You say you find English harder than math, and the essay is for a bigger grade than the math, which is just the weekly homework. So: How do you plan to break down the work?" Then you prompt a short discussion about how working on the essay in pieces each day may be better than waiting until Thursday, or even Wednesday.
Is the sitter doing that level of up-close help, prompting them to think ahead, teaching them to set priorities?
As for the sitter being there to review their assignment books as you mentioned -- I wonder if they are taking the sitter seriously on that front. The sitter may be terrific but that doesn't mean they respect her or him like they do you or dad. They may need this to be done by you or dad, frankly, even if it's later in the evening. They may feel (even if you say the opposite) that the sitter really cannot enforce discipline or take away things if they blow off work. And clearly, having the sitter "make sure everything is done before they are allowed TV or play time" is truly not working -- the evidence is that assignments simply aren't done. How can you work with the sitter on this? Is the sitter really up for being tougher? And I'd tell the kids that the stakes for getting assignments turned in just became much higher, and the consequences will last much longer.
With the one who is not turning in homework and getting 40s etc.--what are the consequences at home for that? Does he actually do it and then just forget it as it's crumpled in a bag or locker, so it's an organization/forgetfulness issue, or does he not do it at all? I hate to say it but if he's not doing it at all, then it might be time for some household changes for everyone. Eliminating ALL screen time (other than for school) from Sunday evening until after school on Friday might help remove distractions. But you'd need to do it for all three kids and be totally consistent and resist a lot of protests....It sounds as if you've used pretty big consequences so far (like losing driving privileges or sports) and that's not working, which I admit would worry me too. What would they really miss if you took it away for a truly substantial time -- think in months or school semesters, not days or weeks? What if they lose something big (would be different for each kid, I'm sure) and then have to earn it back by doing assignments, rather than losing things after the fact when they don't do assignments? That may sound harsh, but for me, getting those good habits into place -- at the very minimum, getting assignments turned in -- might require a "short, sharp shock" for your kids who as you say are "too comfortable slacking off."
About those assignment books: Are these school-issued planners? Does the school set a high priority on the kids keeping up with them and entering EVERY assignment every day IN class? If not -- you will need to set that rule for your kids and then enforce it.
Your oldest with the IEP might be best served if you make time for a focused meeting with whatever staff member is the appropriate one, whichever person knows him, his needs and his IEP best. Your oldest son might need more frequent oversight by someone who's not you or dad (since teens sometimes respond better to adults who aren't their parents). Maybe he needs a daily check-in with someone AT school on his workload and priorities. Is that happening already since he has an IEP? Has the school shown concern about his work habits and academics since he's pretty close to graduation? (I would figure the school would have done so already--? Maybe they have.)