An owner of a home is not required to pay rent. You can move in anytime you wish and not pay rent either.
if probate is closed and the home transferred to the children via deed already you are where you are. If the owners cannot one to an acceptable solution, they either live with things as they are and muddle through the issues it creates or somebody sues to partition the property. Partition is where somebody files with the courts asking them to do what it takes to severe the joint interests. In a single home such as this the only resolution is selling it and dividing the remaining value among the parties.
The big problem with doing this is partition actions are not cheap and the proceeds realized from the resulting auction are generally much less than an open market sale would bring in. After attorney's fees, court fees, auctioneer fees, as well as the typical costs involved with selling a property, some partition actions result in the parties actually having to put money into the pot to settle the matter.
Now, since you did mention your sister is executrix of the estate, that suggests probate may still be open. If so, there is nothing improper about the recipients of the home attempting to settle the issue by swapping other assets in the estate (if there are any) they would also recieve through probate so the sister living in the home could end up with the home or at least having to borrow much less to be able to purchase the remaining interest from the siblings.
If the will actuslly specified the home be split, it would require the agreement of those reciecving shares in the property. The executrix cannot unilaterally remove the heirs interest and grant it to others. If the property was not specifically gifted to the severel siblings but there was simply an equal division of the entire estate, then the executrix is able to distribute assets as they choose as long as each heir recieves the value gifted within the will.
