Wow, even as an insurance adjuster, this one goes on the wall of fame.. (Photos of inconcievable losses...)
Just a guess, but your house repair is going to run you 12k, the Nissan about 3500 and the Supra will need a new right quarter, repairs to the left quarter, replace the hatch, rear body panel and some other parts, putting it into the 4000+ repair range for sure. They are going to tell you it's a total loss, then when you show them the photos, and the miles at 5000 total, they are going to wiggle around and might just fix it. Make sure you negotiate a full repair, blending the paint into the right door so it's going to have a good color match if possible.
I can see from the photos that the Supra was pushed into the Nissan.
I would not be supprised to find dog lady's insurance decides to total your Supra. The cost of repairs, will exceed the book value.
Do not let them take away your car
Keep it, it's worth more in parts than the salvage value they will say you owe them. (I would not let them charge me for salvage, they should give you the car for free, and give you 10k or more for the value of the car.)
Here is the problem. Your not physically injured in this loss. You only have property damage, and the dog lady likely only has a limited amount of property liability coverage. Most states require some minium, but many people only have 50,000 at the most, and a few have thought ahead, and have more. (I carry more myself.) If she has 15k limits, your in trouble as your damages are in excess of dog ladies insurance coverage.
You may need to get your own insurance company involved if you have UIM, or un-insured, or under insured motorist. (This covers you if here coverage is less than what's needed to repair your house, and repair your vehicles. Then they go after the dog lady for the difference...
You don't have to. Your insurance company "Subrogates" this for you, and if need be, will file for a judgement against the dog lady to recover funds. It would also be good to know what your insurance company will pay for the loss in any case. It might be more, and you can use that to your advantage when dealing with dog ladies company.
Getting a lawyer in this case will likely just cost you money, and slow down the process. (Would you like to give 40% directly to the lawyer? Nope, neither would I.) Trying to claim emotional damage is likely not going to work either.
If it was me, I'd replace the entire rear of the car with another one from another Supra. Don't let them total your car. This ruin's the resale value. (You might not have much choice, most insurance companies report to ISO, and places like CarFax get that information.) In this repair, you section out the rear of another supra. Since your car is a targa, this is totally easy as the top section is already "cut" at the targa point. You just need to make sure the shop doing the work does the section right, and sleaves the cut at the rockers to make it stronger than before. I'd see if they can lap weld the floor pan, it would be stronger that way too. Then two part foam the rockers for strength and corrosion resistance. (They have to weld up the area, so every well becomes a hot spot for rust in the future if you do not treat those areas to keep them from rusting.) A good repair here, and your Supra will be saved, and should drive as nice as the day it was made. (Vehicles are assembled to very tight tolerances, and the right shop, with the right frame rack, can put your car back together just like it was, or better.)
Good luck, and I'm glad you and your family are unharmed. The car can be replaced or repaired. It's going to suck, but it can be done. PM me if you have any other questions. I do this for a living, so it's no problem. (If it was me, I'd be asking for a complete tear down, section and replacement of the rear body, then refinish the entire car to color match like stock, re-assembly, and your car is like new again, or better depending on the painter and tech's that work on it.)