Ask your parents if there are any songs that are especially meaningful to them for this dance. If they don’t have a strong preference, don’t be afraid to choose a song you love that’s not a “traditional”
Think about how long you want your first dance, parent dances, and wedding party dances to take. Some people love these dances and consider them a meaningful part of the reception; others consider them just something to get through before the party can really get started. If you’re in the latter camp, consider choosing a song that could be used for both father-daughter and mother-son dance, and have both at one time.
Possibly the biggest challenge in choosing parent dance music is what to do when a parent and a stepparent are both present at the wedding, and the bride or groom would like to dance with both. If relations are amicable, a bride could to dance with her father for one part of the song, with the stepfather stepping in at a prearranged point. The DJ could announce before the dance that the bride is going to dance with two special gentlemen. If this seems unworkable, two separate dances, or none at all, might prevent stress and hurt feelings. When in doubt, an experienced DJ is a great resource. You can be sure he’s seen circumstances like yours before, and will have suggestions for handling it with grace.