Oh Isabel, having dealt with wacky in-laws thru a divorce, I can relate to how crazy-making this can be. Bottom line; You may need to be blunt and remind your MIL over and over that as his Mother YOU decide where and when he goes somewhere. "Weekends or nothing" option sounds fair enough, as long as they play by YOUR rules, not the other way around.
I wouldn't even give the car thing a second thought - its your car to do with as you see fit, certainly not something you need to be stressing out over right now. Sending you good thoughts-