A bride-to-be recently asked what how best to handle the father/daughter dance when there is both a step-dad and a biological father.
This can be a sticky situation. Here is my answer:
In the past, I've had brides in this situation decide to pick an appropriate song and dance with each Dad for half of it.
You could also prearrange for one or both of them to take turns "automatically" cutting in with you once your first dance is over, as part of open dancing time. This is kind of stealthy, placing a bit less attention on all involved but it may not work for everyone.
Another alternative is to start the dancing with Dad #1, after a minute change the song and have your first dance with the groom. Then dance with Dad #2 for a minute or so.
Each of these ideas has its upside and advantages. Hope one of them works for you!