How can i cut together songs for the father daughter dance?

Your DJ should be able to do that.

My dad and I picked a song that was a) kind of long, and b) generally considered romantic, not familial, but she was able to edit it down to a good length and take out the more romantic bits.

Ask your dj because they do that all the time.

Ask you DJ. They should be able to do that for you.

If you have a DJ, they should be able to do that for you. If you're set on doing it yourself, I've done a lot of music editing with Audacity. It's a free program that's honestly really easy to use.