FloppsyLadySally89,

I am not an expert on bunnies...but let me see if I am understanding this:
your dad is a strong believer in the fact that this was an outside bunny and the change in climate would kill him

But, you dad is willing to let you bring him in for short visits and holding and a little playing??

Well, my thought is .... make sure your dad spends quality time with bunny so he can see how wonderful he is and get to know him like you know him
AND
See if he thinks it would make sense to work out a plan allowing bunny to adjust to the temperature difference between the indoors and outdoors. Of course tell him you understand how a quick change could be harmful, but a gradual change...maybe add an hour weekly until Bunny is in the house regularly.
Also you might want to run this idea past your mom first for her support.

Good luck