We were at Big Thunder Mountain a few days ago with a person with a wheelchair. We had not gotten fastpasses for the ride, so we were given a return card to allow us to come back after a wait equivalent to the standby wait. For us, having pushed our relative all the way up to the ride entrance, we didn't think it was worthwhile to leave the area and then have to make the trek up to the ride again. So, we gave up and left. A few days later, we booked fastpasses for BTMR and returned. With our fastpasses, we were sent straight to the exit, and we got on the ride in just a few minutes. So, for us, fastpasses are the definitely the way to go for this ride. Hope your family has a wonderful time on the ride!