Who actually owns each car? In whose names are the registrations, insurance, etc? Who pays for any car costs (car payments, insurance, titles, taxes, license plates and registration stickers)?
If these items are not clearly defined, they should be. If you're going to share a home with 2 relatives, certain things need to be talked out, just like when you're sharing an apartment with a roommate. If your brother-in-law simply says "hey, my car's in the shop, give me your keys", what would happen if you said "no, I need my car to take [your daughter's name] to school and you may not borrow it. Talk to the shop or rent something or take the bus." Or does he ask and beg and you feel bad and give in? Or does your husband or father-in-law put pressure on you to give up your car?
Who owns the home? Do you and your husband pay rent, or the mortgage, or are you allowed to live there rent-free?
Where does your nephew live? Is he reliable? Do you do things for him sometimes? Why do you hate asking him to help with transportation?
Are there no school bus possibilities for your daughter, or do you live in a remote area with no bus service and no car pool possibilities?
I think you need to sit down together, as a household, and talk out a few things. Your father-in-law owns a vehicle that doesn't work. It sounds like your brother (or is it your brother-in-law?) has frequent car troubles. You have a child who relies on you for school transportation. People work quite some distance from home.
So, work out which cars are the responsibility of which people. Work out how to fix the truck. Work out the school transportation issues (either insist that you have your own car for bringing your daughter to school, or sign her up for the bus, or find a carpool, or homeschool her). Decide what happens when one car breaks down (and it might be yours or your husband's) and how to rearrange things when one car is out of commission. Figure out what all the car costs are, and determine who's responsible for them.
Time for a family meeting. Put things in writing so they're clear.