I’m so sorry what happened to you, it had to be terrible to have to face those people and give them a cake… We have all at some point had something like that happen with our cake, but don’t get discouraged, that is how we all learned (on our mistakes).
1. As everyone already said it seems that you didn’t have a proper support underneath the cake, like cardboard circle separating the tiers and supported with dowels.
2. What kind of filling did you use, soft fillings will make a cake bulge between the tiers and also how much filling?
3. I put all my cake into the fridge, (covered with fondant or not) if your home is really hot, there will be some condensation because if the difference in the air temperature, you can sort of say that the cake gets a little shock from the temperature differences. If you do that Mike Mccarey recommends keeping the cake in a cake cardboard box which is placed in a plastic bag and closed while in the fridge. When you take it out remove the bag but still keep the cake in the box until it dries out, the cardboard will take in all the moisture. Otherwise if you want you can also use Sharon Wee’s tip, getting your cake in front of a table fan to dry it out, just be careful…. The only thing to remember is not to touch the cake while it’s drying, when it’s so sticky it will take in any prints and smudges and shapes and stay like that….
Hope that helps, and trust me the next cake will be better… In the beginning I almost lost my mind covering cakes with fondant, even my husband knew to get out of the kitchen and keep away when that dreadful moment would come ;)