NTA. Not even close. Most people make an effort to be fair, and especially so with family for this reason. That they expect something for free tells you everything. Just let the family know you’ve decided to rent during that month, so that you can recoup expenses. They’ll ask how much you can rent it for, and when they hear your answer they will be reminded how lucky they were. That won’t stop them from complaining of course, but at least they can’t play ignorant now.