Does your sister want rent paid to the estate? If so, then you may wish to consider whether you should put in a claim for the services rendered to your mother during her lifetime. When faced with similar circumstances here in Connecticut, I find that a good compromise is to have the child living in the house pay all utilities, taxes, etc. prior to the sale. Please speak with a Kentucky estate administration lawyer for more information. Good luck to you.
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I am licensed in Connecticut and New York and my answers are based upon the law in those jurisdictions. My answer to any specific question would likely be different if I were to review a client's file and have the opportunity to interview the client. Accordingly, I strongly urge you to retain an attorney in your jurisdiction with respect to any legal matter.
In many cases the fact that someone is living in the house and paying for the expenses of its upkeep is an advantage for the estate. You should discuss with your sister how she wants to handle it. Part of the decision would be based on whether you intend to buy her half or sell to a third party. If you are going to sell, you may be able to list the house immediately. You should discuss all of this with the probate attorney.
The above answer is not to be considered legal advice and should not be relied upon as such. You should consult your attorney for specific legal advice as to your individual situation.
Since you mention an executorship, I will assume there was a Will and the two siblings were bequeathed the property. You do not mention how the distribution was prescribed: in equal part or otherwise.
Unless the will specified otherwise or differently, this probably means you are "tenants in common"-- concurrent owners with an undivided interest in the whole property (with no rights of survivorship). The general rule under property law (once the distribution is effectuated and title conveyed, the matter moves from Wills and Trust Laws to Property Law), a tenant in common "out of possession" --not occupying the property--has NO right to demand rent from a co-tenant in possession UNLESS (1) they previously agreed to pay rent (2) wrongfully ousted the coteneant, or (3) denied the cotenant use of and access to the property. Since you continue occupation of the property the latter two exceptions would not appear to apply.
A tenant in common who collects rents from a 3rd party is accountable to the other tenant in common for any profit from the lease arrangement.
Again, this is subject to the language of the Will. There are different types of concurrent estate with different rights and obligations, so it is in your best interest to speak with an attorney who can review the language of the Will and advise you as to each parties' rights and obligations. There may also be state laws that touch on this subject, so a local estate's attorney is your best bet for the most reliable advise. Good luck.
This answer is provided for informational purposes only and it is not intended as legal advice. Additionally, this answer does not create an attorney-client relationship. If you wish to obtain legal advice specific to your case, please consult with a local attorney