I do a bit of traveling and have a couple of suggestions. To begin with, I do not know anything about the Mexico part, but the following is good for the drive out / fly back part.
I have a lighweight nylon windbreakers that came with a small stuff sack. (usually easy to find in hiking/backpacking stores). It is small and light and usually I include it any time of the year when I pack for a trip. It has come in very handy when the weather has changed. If you want to pack light on clothes, lighter garments that can be layered are a better bet than a light shirt and a heavy coat. (Don't know what time of year you are leaving NY.)
Second, I have gone on trips and decided to bring more stuff back than I left with. On the other end, buy a small cheap duffle bag. Wrap whatever you cannot include in the carry-on backpack in your dirty clothes and check the duffle on the airplane. Of course, before you leave check on the airline webpage to see what cannot be included in carry-on baggage, but what can taken in checked. That way, at least in the US, you could take a knife or multitool as long as you shipped it back as checked baggage. (Do not check anything that you would cry over if it was lost.) I assume that you cannot take more because the car is packed to the roof with your friend's stuff? If so a empty duffle can be squeezed in even if you have to sit on it.
Plan B: I have done this before too. If you really want to take something on the drive, like a knife, that you cannot take to Mexico or on the plane, mail it back home from the other end. Again, check before you leave on what is acceptable for shippment. Do not walk into the Post Office and try to mail a Glock.
Final suggestion for travel, always stash away a little cash in small bills and some change.