My suggestion would be to put some nasty *** trim on the engine, gungy wheels, and a bunch of trash in the interior. Hammer a plug gap or two shut. If you don't have the stuff, maybe a FABO reader in the area can loan it to you. Then take it to Carmax and get them to give you an estimate. Pretty sure it will be far lower than what we think it will be AND it will be in writing by an appraiser. The number should stand up in court. You can laugh later when they buy off on it.
It's tough to be where you are right now. I can't imagine what it would be like to have small kids in the middle. Mine were gone. It does get better. IMO, you don't get over it, you get through it. Just keep putting one foot in front of the other for now.