So you drive with your own car right?Did you car was financed by bank?Did you have title with you?My is financed by bank so don't have title?Do you think renting a car will be a problem??
Yes, I landed in my own car. Had title of car with me as well. I believe landing in a rented car shouldn't be an issue. As a matter of fact, a lot of people prefer going in a rented car. You should be fine. Good luck!
I am not aware of what happens at all the borders across the United States. However, if you go by land, my understanding is that nobody cares if you are leaving the country. It's the country that you are entering where security officers will be most concerned. In my case, I wasn't stopped. In fact, there was no booth at all to even watch or stop who is leaving the country. While re-entering the United States though was a different story all together. It felt like I was somewhere in Army base. Lots of Border Security Officers. The one I ran into unluckily was quite rude (you can read about that in my landing experience). But I am sure not all are same.
Anyways, even if somebody's there (while leaving US) to ask questions, never surrender your I-94. Just tell them that you are going to complete your landing formality and will return in whatever time you are planning to return and will need I-94 to re-enter. This is specially important if you are planning to use AVR.