I'm going to be honest and then prepare myself for your responses (oh, I lurk alright- I know how you girls can be with honesty

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I am not close with my father- at all, never have been. My parents are still married, it's not a matter of abuse or neglect or anything like that at all, we just are plain Not. Close. Period. My father had extremely neglectful, alcoholic parents. He was NEVER shown physical affection, or given any words of positive praise in his life, and rarely even had food to eat. Therefore, he was never that way toward my older brother and myself. He would show us affection and that he loved us by buying us things (sometimes over the top) and by overall just making sure we never went without. He was a harsh disciplinarian, but never abusive. Now onto the real dilemma here--
FI very much wants to do a Mother/Son dance with FMIL (otherwise I'd just cut the parental dances completely). I understand that completely. However, I do not want to do a Father/Daughter dance. I know it would make my father EXTREMELY uncomfortable (not purely just because of dancing with me, but because of the center-of-attention thing), and make myself the same. I am in my mid-twenties with 2 children so of course I support myself financially and have been out of my parents' house for 7 years, so the symbolism of being his "little girl" and "giving me to another man and a new life" isn't really, well, relevant.
I don't know what to do. While I know he would be uncomfortable with the dance, I don't want his feelings to be hurt or for FI's family to wonder what's going on if we have no Father/Daughter dance. I'm thinking maybe I should just pick a short song and do the dance anyway.
My dad knows I love him deeply. It's easier for us to communicate those sorts of feelings via cards on birthdays/special occasions. My birthday last year, he wrote in a card how proud he was of me and the way I'm raising my girls and who I've become as a person. There are no negative feelings between us, just not any sort of closeness.