It sounds like the parents aren't paying much attention to what their daughter is doing. Still, I would tread VERY carefully for now, as sometimes parents can get very defensive. Since you don't know them well, you don't want to start off on the wrong foot. Trust me, I've seen my mother have wars with the neighbors and it can get ugly and nasty and extremely childish, and it all started over them taking offense to something almost as innocent as what you're talking about. Wars with neighbors are not pretty, and in this housing market, you're pretty much stuck with your neighbors.
If it were me, here's what I'd do...
1) Establish a good relationship with the parents as quickly as possible. Perhaps invite them to dinner, or make them a casserole for a night when they're busy unpacking and don't have time to cook. Be the best, most thoughtful neighbors possible, as long as you're not going past your comfort level. Go out of your way to look for ways to offer help or offer to lend them something, though not anything that you value so much that it would cause hard feelings if it were lost or damaged. (e.g. "Oh, you're painting? I have some canvas tarps and painting supplies if you'd like to borrow them.") If you dare, you might even offer to watch their daughter while they paint one afternoon, etc.
Basically, build rapport so that when you do need to talk to them about their daughter, you'll know them well enough to guess their reaction and know the best way to approach them.
2) For now, I would stick to talking directly with the daughter to set limits. Since the parents aren't paying much attention, they'll probably never know anyway.
With the car, I would say, "My son is only allowed to ride it for 30 minutes a day, so it's only fair that his friends can only use it for 30 minutes, too." Then when the 30 minutes for both of them are up, it goes away and the battery comes out. If she won't get out of it, say, "Sweety, I'd really hate to have to go tell your mom that you aren't listening. You need to get out of the car so we can put it away now."
Keep your gate locked if possible. If not, try not to keep anything back there she'd be interested in, and watch carefully. Maybe wait until you catch her back there again to say something. Same goes for her coming in your house. Do NOT put yourself in a position where you're accusing her of lying. You may be sure she was in your house, but you didn't see her, so there's room for doubt in the parents' mind. If she tells her mom she wasn't in there and you didn't believe her, mom may become defensive (My daughter doesn't lie!).
Do you have pets? If you have a dog, that could be a legitimate and understandable reason to casually mention something to the parents now rather than later. (e.g. "I noticed your daughter coming out of our backyard the other day. The latch can be tricky and sometimes kids can't close it properly. Our son and whole family would be devestated if the dog escaped. I think it's best if she doesn't go in our yard without us.") Unless you can think of a specific reason like that, I'd wait to say something...first to the daughter, then to the parents only if she keeps doing it.