Sprawdź dwie daty nie było między dwiema inną datą + MYSQl

Wypróbuj coś takiego

SELECT 
    tbl_room.room_no, 
    tbl_room.type_id, 
    tbl_room.id,

    tr.id as reserv_status

FROM tbl_room

 LEFT JOIN tbl_Reservation tr ON tbl_room.id = tr.room_id AND 
           (
             (tr.checkin_data <= "'$checkin'" AND tr.checkout_data >= "'$checkin'")
             OR
             (tr.checkin_data <= "'$checkout'" AND tr.checkout_data >= "'$checkout'")
           )

 WHERE 

 tbl_room.type_id =1  AND tr.id IS NULL