I'm hoping to do a brother-sister dance as well (it depends how overwhelmed my brother is because he has autism). We both love Toy Story and it was a staple of our childhood so I think it would be really cute to dance to "You've got a friend in me".
You should look up We Were Just Kids by Clean Bandit! If you're looking for a really great/sweet/loving sibling anthem that you could either sway to or just have a fun time dancing to, its a good mix of both.
If you don't mind a touch of country, My Wish by Rascal Flatts actually brought a tear to my eye. Another good choice is Whenever You Remember by Carrie Underwood (still a touch country but not super much so).