OP here. To answer some of your questions, our party constisted on two small children and four adults. My MIL had just had hernia surgery and I was in charge of holding backpacks,shopping bags containing Christmas ornaments and making sure our two little ones didn't get lost in the process!! So that only left my disabled FIL and DH to handle all the checked luggage.
When the Magical Express dropped us off at the aiport, it looked like a ghost town!! There was no one in sight! We just thought there was no one there because typically everyone's checked luggage has already been brought to the airport, so there would not be a need for Skycap assistance. Anyway, we paid for two carts and drug them across the airport. There were signs on the 1st floor that said there was a Southwest checkin desk on that floor. So, we walked and walked and walked until we got to the EMPTY Southwest desk!! Then we took the elevators upstairs to the correct Southwest check-in desk.
We've used Magical Express the past 6 trips and the whole process worked seamlessly but of course on the trip that I plan for my in-laws, this happens!! Also, because of the cold weather, we had twice as much luggage as we normally do. Oh well, we survived

but from now on, I know to expect that this could happen.