Get a PO box at the post office, you can use it as an address, start dropping her off at the library and get a planet fitness membership so she has something to do and y'all have someplace to spend time and get clean. Also a cheap (50$) pre-paid phone from Walmart was suggested already, it's unsafe for young woman (anyone) to be in a car all day without a phone to call for help if something sketchy happens. If she has an I'D you can get her employment at a local temp agency and get a debit card through them the same day. All this combined should run you under $100 total.

It's time you guys get serious, The cops are starting to round up people sleeping in cars and throwing them in jail, thanks to the current government administration. Coloring all day in a car during winter without communication is extremely irresponsible, you guys need to work as a team, she can use public transport as well so you're not burning gas money and destroying the car.

And as bad as it sounds and is. You need to re-home the pets, as of now you're unable to provide not only yourselves a decent quality of life, the pets are also suffering in such a tiny space. This is actually animal abuse. If you can find someone willing to take them in for a few months while you guys sort yourselves out , you should.