Adverse possession is probably not the right way to deal with this. Try to negotiate with your siblings to buy out their share of the house.
I am licensed only in Texas. Offering information of a general nature in response to a question is not intended to be legal advice in your state.
To provide a more detailed answer, I assume that the probate of the estate was never completed. Therefore as a child of the deceased you should have the right to open the estate - if your siblings renounce their right to do so and they also are willing to make an agreement to waiver their share of the estate you should be able to accomplish your goals. This is a much simpler process, especially if there is agreement among the family, than what you propose. Hire competent probate counsel to assist you.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature. Visit Steve Zelinger's website: http://www.stevenzelinger.com/
There are not many facts here to go on. Adverse possession claims must be "adverse". You must be occupying the real property without the consent of the owners (you and your siblings). It may be difficult to carry that burden of proof. Why there was no probate on your father's estate 15 years ago is the big question. You are never going to be able to establish ownership without some type of administration or agreement with your siblings and to advise you on that a lawyer is going to need a great deal more information. Do not delay in addressing this problem. It has been made substantially more difficult by the delay so far.
DISCLAIMER: This is not specific legal advice and does not establish an attorney/client relationship.