People often ask if they can keep homes, second homes, cars, boats, tax refunds, etc., when they are contemplating Bankruptcy. I always tell them they can keep what they want of they can pay for it, or if the equity or value is protected by an exemption in their State!
There are two types of Bankruptcy for most individuals. Chapter 7 (liquidation) and Chapter 13 (payments are made to a Chapter 13 Trustee to be distributed pursuant to a Plan you and your attorney draft). To determine of you get to keep the property you have to know two things…
1) What is the equity in the property? (I.e., what is it worth minus what you owe on it).
2) Will the exemption laws that are applied to the property protect the equity?
Bankruptcy is much more concerned with equity than it is with debt. If you have no equity in a rental home the Trustee in a 7 or 13 does not have an interest in the property and you may keep it.
If you owe more on the vacation home than it is worth you may be able to use Bankruptcy to reduce the amount of the debt, and again, keep it.
When you have equity in something that is not protected by an exemption then that is an issue that a lawyer must evaluate. See an attorney right away before you act.
Disclaimer: This answer does not constitute legal advice. I am admitted in the States of New York, New Jersey and Massachusetts only and make no attempt to opine on matters of law that are not relevant to those three States. This advice is based on general principles of law that may or may not relate to your specific situation. Facts and laws change and these possible changes will affect the advice provided here. Consult an attorney in your locale before you act on any of this advice. You should not rely on this advice alone and nothing in these communications creates an attorney client relationship. The opinions expressed herein are those of the author only and the fact that he has worked as an Assistant District Attorney; State Supreme Court Clerk; Special Assistant United States Attorney (Hawaii); Assistant Cornell University Counsel or Judge Advocate, United States Marine Corps should not be relied upon to assume that these statements reflect the policy of these organizations.
You are going to have a problem with the equity in those homes. My understanding of the New York bankruptcy exemptions is that they are very very low (50K single/100K married couple/125K limitation on homestead), so, in a chapter 7 you do not have enough exemptions to cover the equity that you have in the homes.
You mention that your name is "on the deed" of the other house. That means you have an ownership interest, irregardless of your reasons for having your name "on the deed". Ownershp is ownership, although the presumption is that you only have a proportionate ownership with your parents.
A chapter 13 may be your best option, depending on your complete financial picture and what it is that you want to do with the bankruptcy.
Based on what you yourself perceive as the issues, you really can't afford not to retain an attorney to help you take stock of your assets, debts and income, to come up with the best solution, and to help you through the complexities of bankruptcy law and procedure.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.