Contact them one last time, and try to get them to refund the extra day, and personally, I'd be going for the original rental fee as well (everything you paid to them) for the headache of the whole deal. It's their truck and they are required to maintain it/inspect it BEFORE the customer takes it.
If they refuse to meet you where you are ok with it all, then do a chargeback with your bank. Give the bank every single detail you can, including EVERYTHING you listed here, and any other info you can remember/have. Chargebacks almost always go in the customers favor. I personally would have been LIVID if I was forced to sleep in a moving truck in a isolated, unsafe rest area (I'm a woman though, so these things can be scary for me).
Also, not to pile insult to injury, but next time, make sure to go back inside, and make them give you a whole new truck, to avoid anything like this in the future.
Not to diminish anything enlisted woman have gone through, but this is by no means unique to military service. I am a women, who works in a very male dominated field, and the hostility, belittling, sexism, etc I have to endure, that my male counterparts don't is massive.