This is not necessarily a bad idea. I haven't rented a car in a while, but $10 a day sounds really cheap. If you're able to snag that price with no strings attached, it might be worth the peace of mind. Our car is newer and is under warranty, so we feel comfortable with it, and it gets good gas mileage, but if your car is older, has issues or isn't under any type of warranty, I certainly understand the desire to rent something reliable. Plus, in some cases, I imagine you can actually save money by renting a smaller car vs. driving an SUV or other gas guzzler.
I would carefully examine the fine print, though, because something does not sound right.
I am not a camper and would never suggest camping just because I'm not into it. That doesn't mean it's not a good idea. Plus, you wouldn't want my advice anyway, since I don't know what I'm talking about. ;)
Try Priceline's Express Deals to find even cheaper rates on hotels, though. They can be cheaper than you think if you aren't picky. We've stayed in cheaper hotels and have overall been fine with it.
Stock the car before you go. What kind of stuff do you like to eat at home that's easily portable on the road? Granola bars, cereal bars, applesauce cups, fruit cups, pudding cups, etc. are good because they keep well even when they aren't on ice. Bringing a cooler with bottles of water, sodas, energy drinks, sports drinks or whatever you and your crew drink.
Stop by grocery stores and get rotisserie chickens, fried chickens, etc.
Not a bad idea.