Father daughter dance

I was kind of in a similar situation, and I get what you mean for sure. I almost went with "Landslide" by Fleetwood Mac, but ultimately decided on a different song. I'm not sure if it fits your music vibe, but I definitely feel like the lyrics "get it" (if that makes sense)? Best of luck to you, I know the right song is out there and you'll find it! :]

It not traditional, but maybe an instrumental song would be more fitting?

I feel like finding the perfect song is always tough. I also agree with PP about asking the DJ/Band

Since you two aren't close, I would just pick song with neutral words (i.e., not a love song) that you like the tempo of for dancing. Don't try to force a song to fit your relationship; that sounds too stressful.

My dad is not good with emotions. So we decided to do something silly along with my sister. The two of us dancing together at my first wedding was awkward and a little weird, so we decided to just give in to the silliness of the thing and I think we will have better memories. We're going to do the Time Warp from Rocky Horror Picture Show, and then invite other people to join in towards the middle. It's more us.

Something more upbeat takes some of the emotion out of it. We danced to "The Way You Look Tonight" by Sinatra. It was fun!