OP, I'm sorry you're in this situation, but I'm afraid you're not going to be able to refinance that loan for a significantly lower rate.
A timeshare loan is not, from a bank's point of view, like a mortgage on a house. A house has some resale value, most timeshares have next to none. Many, if not most, banks, won't even finance a timeshare. If they do, you'll get a very high rate that's pretty much the same as what you got thru Disney.
If you don't pay your mortgage on your house, they can repossess the house, and hopefully sell it for something at or better than the amount left on the mortgage.
If you don't pay your timeshare loan, the bank takes your timeshare away - and in most cases, they'll only get a few bucks for selling it.
DVC is a little different and has some resale value, because Disney is currently propping up the resale value with ROFR. But….it's still a loser for the bank. Here's why:
I don't know which resort you bought, but unless it was VGF, it's very likely that by buying direct from Disney, you paid much more than the resale value of the contract. For some resorts, you may have paid as much as double the resale value. If you financed the entire purchase, there's a good chance that you're seriously underwater on the loan. Meaning, the amount you owe on the loan is more than you (or the bank) could get back from selling it. Potentially, thousands of dollars more. That's a big risk for the bank, and that's why they won't finance at a low interest rate.
Since you don't own a home and so don't have the option of a home equity loan, you have a few options that I can see.
1) Look around for a timeshare loan. Even if you only save a couple of points off the interest rate, at least it's something. Or...
2) Sell your contract, and purchase a resale contract - and don't finance it. You'll have to do the math on this one, and figure out whether the money you lose on the sale is more or less than what you'd lose by continuing to pay that super-high interest rate. If you can't afford to buy without financing, then just rent from other owners. Same vacation, without the long term financial commitment. Or...
3) Reduce the amount of interest you pay by paying the loan off as fast as you can. Make extra payments towards the principal every month.