This thread confuses several entirely different issues but comes down to the bottom line that OP's niece was not a UM and was responsible for her own IRROPS acommodations. Whether and how those are paid for is a different question.

Few properties will rent a room to a <21 under any circumstances. Thus, OP was lucky that there was a property at MIA. But, for planning purposes, presume that there will not be a room to be had (however booked and at whatever rate).

The second that OP's niece was stuck, the smart move would have been to find her a room and to sort out reimbursement later. She is lucky that there was a room to be had and OP should understand that at most major airports, the carrier would have been unable to help at all.