Problems with Inactive Households

For cars, if you have the SP Money add-on, you have a couple options here:

NRaas > SP > General Options > Options: Money > Options: Purchasing

Specifically, you could block SP from buying certain cars, or set the minimum amount in family funds for a vehicle purchase so high that none of your sims can reach it.

However, the game itself will sometimes buy cars for households when sims need to get somewhere. If you want to stop this too, you can add Traffic and use this setting to force them to take taxis instead:

NRaas > Traffic > Routing > Always Use Taxis for Inactives Lacking Vehicles > True

For cars the sims already have that you want to get rid of, you can delete them with MC. I don't think you even need to switch households: just click on the lot where the sim in question is currently located, while they have the car in inventory, select:

NRaas > MC > Object Stats > Inventory

Then choose the car and flush it. If that doesn't work, you can move the car to one of your sims' inventories and flush it from there. Click on the othe sim and select NRaas > MC > Basic > Transfer From > , then choose the car. The Object Stats command definitely works for your own sims as long as they're on the lot you click on at the time.

For the homework issue, I see that in my game too and haven't figured out a way to fix it. I think in my case at least the issue may be that I've prevented progression for my rotational households, so they can't gain school performance, but they can lose it by skipping school entirely. Some of my households' children still have perfect grades, just as they did when I left them; others have perfect Fs.

I don't know whether you've blocked progression too, but you could try enabling it for children only, in a higher-priority caste than whatever you're using for your protected households, and see whether the kids' performance goes up or maintains itself better than the teens' performance. If you do allow progression for teens too, make sure to block Allow Find Job for them unless you want them all to have part-time jobs.

Personally, I just fix school performance with MasterController when necessary.