You are in a tough spot. Absent a writing establishing your entitlement to the apartment your rights are very limited. Your relationship with your family is apparently such that you don't trust their assurances and you don't think they will sign anything. Prodding them may have just the opposite effect from what you want. You need the advice of a probate lawyer in the place where your father's will is being probated. A skillful litigator who is also a skillful negotiator may be able to help you but it's a tall order.
Any opinions stated in response to Avvo questions are based upon the facts stated in the question. Responses to Avvo questions are for general information purposes only, and should not be construed or relied upon as legal advice.
I agree with Mr. Brophy's assessment of your situation. You should contact a probate attorney where the Probate is taking place. You should gather as much information regarding the circumstances you have described so that you can have a thorough and in depth conversation with local counsel. Best of luck.
When responding to questions posted on Avvo, I provide a general purpose response based on California law as I am licensed in California. In reviewing my response, you are specifically advised that your use of, or reliance upon any response I provide is not advisable. I do not have all relevant background details or facts related to your issue / matter, thus I am not in a position to give you legal advice. Further, your review, use of, or reliance upon my response does not establish an attorney-client relationship between us nor does it qualify as a legal consultation for any purpose.