In all the times I have flown, and gone to Disney, I have only had difficulty a couple of times with luggage. It has been with a variety of airlines, and not one in particular. Years ago, about 1980 or so, we were flying Eastern airline from Columbus, OH to Gainesville, FL. We had a short connection in Atlanta, and our bags didn't make it. Fortunately, we were staying at my parent's house, and they delivered our bags to our door about 24 hours later.
By far, the most aggravating experience was with ATA, when I was flying with my son. The airline made us gatecheck our carry on bags. We had been delayed at the check in counter for about 1.5 hours due to understaffing, at about 5 am. We just barely made it onto the plane, and there was no room in the overhead bins. Of course, I had things in the carry on bag that I didn't want checked, so it totally steamed me, but, I did what they said. When we arrived at MCO, our carry on bags were no where to be found. I was in the customer service office, nearly in tears, reporting the lost bags, when my son noticed that they arrived on the carousel with the bags from the next flight, which was an hour later. Why they would gate check our bags, and then put them on a different plane, is beyond me.
Then, there was the time we were flying from IND to SNA via DFW. When I was booking the flight, I chose the earlier of two flights that were an hour apart. Once again, the airline chose to put our luggage on the next plane. Once again, our bags were not at the airport. This time, I was going to a conference in San Diego, and had my husband and son with me. I have to admit that the passive-aggressive side of me toyed with the idea of letting the airline transport our luggage from Santa Ana to San Diego, but, I decided that I would much rather have my luggage than take revenge on the airline.