Airport in Chetumal is really not only unfunctional, but also too small.
We had to wait for one hour for our luggage to "arrive" to the band, so we could pick it up and then just leave. But oh surprise... it took us around 15 minutes more to wait on the line to leave, because if you want a private airport Taxi, you have to make a line... and even worst... we didn't know that these insider Taxis were so expensive and that at the end you have to "share" your taxi with other people traveling to the same area! Yes, you have to share the taxi with other strangers (also air passangers) so at the end, you pay for a taxi service, but it will not be entirely for you (and your family).
During our holidays, we learned by a local Taxi driver that normal or local regular Taxis are not allowed to enter to the Airport zone to pick up passangers (because it is a federal area), so these poor guys are only allowed to leave passangers at the airport but not to pick up people. So it is a Monopoly running the inside Taxi Service at the airport.
My suggestion: Before traveling to Chetumal try to hire a Transfer / transport service with anticipation, maybe with your hotel. If you can't get this service via your hotel, I strongly recommend you walk away off the Chetumal Airport (around 300 meters from the airport exit) to the "Glorieta Maya", there you will see local taxi drivers passing by, waiting to pick up tourists, and while the Monopoly of Private Taxi Service at the airport charged us 350 pesos from the Airport to Bacalar, a normal drive costs 200 pesos (that is what our local taxi driver charged us when he took us from our Hotel in Bacalar to the Airport and we did not have to "share" our taxi with other strangers).
So please... Do not get fooled by the monopoly of private Taxi service inside Chetumal's Airport... walk away 300 meters and pick up yourself a local taxi driver, it is way cheaper and at least you give some work to local people instead that to this monopoly.