Every state's law is different, so you will need to check with a Florida lawyer. If this were California, you would not be required to pay rent unless there was a written agreement saying you would do so (see California Civil Code section 843). The laws may very well be different in Florida.
The information you obtain at this site is not, nor is it intended to be, legal advice. You should consult an attorney for individual advice regarding your own situation.
In Florida the personal representative of the estate has an obligation to marshall or try to collect all the assets of the estate and make sure nothing in the estate is being damaged, destroyed or wasted. For instance if the home were vacant, the personal representative would have to make sure lawn gets mowed, the property is secured etc. Before the home is formally transferred to whomever it transfers pursuant to the will, it is the property of the estate and there may be some argument that the estate is entitled to be compensated by whomever is using it. Having said that, any nominal fee this might be (assuming this isn't a million dollar beachfront mansion with pools, etc.) would be offset by the service you are providing to the estate for looking after the property and keeping it secure. Keep receipts of repairs you're doing and how you're improving the property.
Most importantly, just try, try, try to all be reasonable. Things like this tend to spin out of control when hard feelings and emotions get in the way of the real issues. I've found that rather than adamantly saying, "I don't have to pay anything" or "You most definitely have to pay rent"...if the family can just sit down and see things from each other's perspective a little give and take goes a long way.....all communication should be started from the perspective of, "What would dad think about they way we're handling this?"
I agree with Mr. Weidner's thorough answer. If the home was your father's primary residence, the home could be considered "homestead property". An order confiriming this is usually not available until several months into the estate, so there is a period of uncertainty. If the home is homestead, and is left to persons who are related (like your father's children), it is not part of the actual "probate estate", and is owned as of the moment of death, but the three daughters. They take title as "tenants in common", meaning each has a right of possession and each has the duty to share in expenses. In many cases, the person in possession does not owe rent to the other owners if they did not force the other owners out of possession. It is probably fair to say that the person in possession should pay utilities, routine maintenance, and other expenses based upon their use of the property. I would reiterate Mr. Weidner's advice that it is best to first consider what is reasonable and fair to everyone, and work together whenever possible. Legal fights over maters like rent due from one sibling to the other often cost more than the money involved. When the heirs of the estate don't agree, it would be advisable to seek at least a consultation with an independent attorney to review the situation and see where you stand.