That 82% utilization is what will likely kill the financing options. Remember 90% is considered maxxed out.
From my experience I saw increases in score dropping below 70%, 50% and 30% Utilization.
You may want to look into SoFi.com and see if you can get a pre-qual offer (soft pull). Usually if they approve a pre-qual you should be good to be approved with a HP.
If you could get a personal loan to cover much of your credit card debt, your scores would really take off (even though you would have the same debt, revolving versus installment are viewed differently).
OP, you are in no position to take on further debt at this time given your 82% utilization on your credit cards.
I think Appleman has a great idea about converting the revolving debt to a SoFI loan, if you qualify. The only caveat I have is this: will you run up your cards again? If not, then I think it is a great idea to get on a plan like the SoFI loan. If you don't get approved, then try the snowball method.
If you can paydown/payoff the credit cards substantially without the SoFI loan (snowball method), that might be a better solution. Then look into getting a vehicle. I know you said you had to have one now due to your family size, but putting yourself in a long term high-interest rate loan (if you are able to get approved) will only hurt your financial future. This is how repo's happen - vehicle loans given to those that are already in over their head. I am not saying this to be mean - I happen to be in one of my paydown periods too before I buy my next vehicle. Everything is timing. Once you get to where your finances are in better shape, then you can get a better loan for the vehicle you want.
I understand that you've made your decision, but I'll just add my input from the standpoint of an outsider. With CC debt of $12k and $7k upside down on the trade in. It seems that you REALLY aren't in a position to take on even more debt. I wouldn't attempt to buy more expensive until your current debt is under control. Pay off the credit cards and eliminate the negative equity unless the new vehicle purchase will have a lower interest rate than the old vehicle.
Is the Equinox your only vehicle? How many people do you tote around on an every day basis? How often are you taking family road trips?
I don't feel like the occasional road trip justifies adding to your debt. Even more if the interest rate is going to be greater than 2% which it probably will be.
Congrats on getting the Prosper Loan. Of course the big thing is to avoid bringing back in more credit card debt.
I know for me, finally utilizing a budget was a game changer. I am still a fan of YNAB.com but there are many budget programs out there....
Budgeting helps change your perception of money and debt. I know I always viewed an open credit line as an invitation to spend. Now I think in terms of the daily and monthly cost of credit, utilization and debt to income ratio.
Thought I would add my 2 cents. In the early years of my married life we got into the cycle of having negative equity roll from one car to another as our needs/preferences changed and we traded in existing cars for new ones. My experience is that this is a terrible practice. Eventually you have to pay off that extra 5-7k that got rolled into the new deal and why you can have a payment that is affordable you are driving a car that has and will have a ton of negitive equity for several years. Now we plan carefully when it comes to our car purchases and we don't go for a new car until we have positive equity. This has forced us to be a little more disciplined but has opened many doors for us in terms of options.