So, all the recipes I find for rum cake call for a bundt pan, but I have a bride that wants it for the top two tiers of her wedding cake which is square. Will I have any problems putting those recipes in square pans?
You should be OK with small pans. You might get some extra humping, depending on how full you fill them. Have an extra batch of ingredients handy just in case you have to cut off more cake than usual. It's OK to build these tiers from three layers if each layer is 1" or just a little more.
I would line bottoms with parchment but not grease the sides (regardless of what the recipe says) because you are not concerned with getting a cake out of a fancy fluted pan.
For future reference: You might have problems with any size larger than 10" square pan--I would expect the larger cakes to fall slightly in the middle.