2 things ..
1) I believe you got misinformation, or may be misunderstanding about a 2nd mortgage. They have as many rights to a property as a primary (1st) mortgage holder.
2)You cannot keep anything with value it in as your own with minor restrictions to this. The courts have the rights to decide what you can and cannot afford. It isn't up to which payments you want to keep.
If there is any equity (in the DVC verses what you owe on it), affording the payment doesnt matter. If you owe someone (like a second mortgage holder, or credit cards ect)which it shoulds like you do. The equity or $$ belongs to the others you owe the $$ to.
Also I work in the mortgage field. Lenders can choose to remove a second or even 1st for that matter from title. Even allow a person to keep only their 1st or have a free and clear home, (pulling their second (or 1st) off title. ... AND they only do this if they get enough $$, IE you settle with them to release that lein. ... Giving them say 1/2 or 3/4ths of what you owe every lender and every market has a $$ amount, but no one willingly lets a loan go, without trying to get it. I am assuming it is larger than 10K. Talk to an attorney.
Otherwise the second lein holder has the right to force a foreclosure. Even if you pay your 1st lein on time. They will not just "let it go to BK". Wash their hands and let you keep your home, as well as your time share. They want the $$ you spent on the home you bought.
Assume you owe 100K on a 1st mortgage and 50K on a second mortgage and your home is worth 120K. They will take even 5,000$ after attorneys and closing costs on your home and 2K on your equity in DVC over letting you keep both and not getting anything. If you signed a contract to pay a debt, (mortgage) they gave the $$ to someone and will want it back. They will try to get as much as possible. ***
Lastly, a BK court will not liquidate and wash credit cards allowing you to keep a vacation home monthly payment. Even at owing exactly what it was worth or more, they would force a sale, or send back to Disney. After BK they look at payments and make sure you can afford bills. They would require you to pay a credit card or installment (car loan) payment over a second real estate property. They use logic on what you should do, not what you want to do. Once you file your hands are tied, you have little to no input. You cannot state I cannot afford my second lein on my primary residence or my credit cards I already spent the $$ on, but I can afford a second real estate loan payment for vacations. Won't fly. Call an attorney.
*** I am not an attorney, I do however work with a mortgage comany and if I was in charge of your file this is how I would proceed. I would try to make as much $$ back from your file, as I could noting we could not take everything you owed. We would require a full liquidation for any $$ even 1,000$ it wouldn't matter. I cannot see ANY lender washing there second lein as you are impling is possible, they would force a sale of the primary residence property, and the time share.
Call an attorney before doing anything EVEN selling, as this may make a difference. I think there is a misunderstanding on what BK is, and how it works and even the 3 real estates loans you currently have. I wish you the best of luck, it is a freaking tough job market right now.