Disclaimer: I am an attorney, but I am not your attorney. This is not legal advice, just friendly information.
I see three issues with this arrangement. First, it's worth reconsidering whether the LLC is the best arrangement. LLCs typically don't qualify for property tax homestead exemptions, and pay more for mortgages and insurance. Good insurance is always the first line of defense.
Second, the primary purpose of having an LLC is asset protection for the members, but that only works if it's treated like a company. If some of the members live there, the line between personal and business property starts to blur.
Third, members have a fiduciary duty to the company. If there were a dispute between the members (hopefully that doesn’t happen with family), a rent-free arrangement could be characterized as self-dealing (taking personal benefit from company property). Rent doesn’t necessarily need to be paid, and it would be a double taxation issue, but a contract outlining the arrangement signed by all members would certainly be helpful.