You're going to want to spend a little time locating and visiting personally with an area probate lawyer regarding these issues, as your question raises more questions than you might think. From the sound of things, nothing was done after your father's 2002 death in the form of any probate proceeding. This, if true, may raise some time limitation concerns if your father did or did not leave a valid Will. If an administration did occur, property remaining in the decedent's name 9 years after death can generate some problems, and you're seeing that now.
Your facts also raise the issue of whether or not you and the "paying siblings" gave up your right to rent from the non-paying sibling when you failed to ask for it. It's difficult to determine if you consider yourself the executor because a Will exists or because a court appointed you to the position. As the court-appointed representative of the estate, you would have been bound only by the terms of the Will and the probate laws of the state with respect to the limit of your authority as executor. If a proceeding hasn't taken place to appoint you, I can't imagine you having any more authority than any of your siblings.
This answer does not constitute legal advice. I am admitted to practice law in the State of Texas only, and make no attempt to opine on matters of law that are not relevant to Texas. This answer is based on general principles of law that may or may not relate to your specific situation, and is for promotional purposes only. You should not rely on this answer alone and nothing in these communications creates an attorney-client relationship.
You need to speak to a probate and/or real estate litigation attorney.
If your father has been dead since 2002 and if the estate was properly handled through probate, then it is relatively unlikely that it is owned by the estate and more likely that you and your siblings have some other form of joint ownership such as "tenants in common" or "joint tenants." In other words, you may well not be the executor, at this point.
Either of those types of ownership permits one or more tenants to "sue for partition," which will usually force a sale of the property and the division of the sale proceeds.
Do not do anything without speaking to an attorney, as you can easily get into trouble here. I won't guess what the possibilities may be as I don't know the details. But if you track down all your records (including the probate file) it should be relatively simple for an attorney to explain your opinions.
I am not your attorney and am therefore giving only general advice. DO NOT rely on this advice to make your decisions. Please see a local attorney, licensed in your state, for further advice.
You need to finish your job as executor. If the property is in Massachusetts, the heirs own it, subject to the right of the executor to sell it to pay debts. The tax bills should not have been going to the estate, but to the heirs. If you had finished your job as executor, you would have filed a final accounting, and your problem would simply be one of owning the property jointly and who is to pay.
So you need to finish your job as executor, and then you need to cope with the problem created when siblings wind up owning property together. It will not be easy. A counseling attorney can help you decide on the next step to take. It may be that the fact that you have been receiving these bills as executor will actually help you.
But you definitely need to move quickly, before the town takes the property for taxes.