This is a brilliant beginning. I love stories where people take something from canon and AU it -- Rose saying no twice is something that I actually haven't come across. And poor Nine! I can just see in my mind the look that crosses his face when Rose says no the second time. Rose must be quite strong to hold up against that face; I'd have broken and said yes.

And I was giggling at the mental image of what the Doctor's expression would be when he flips a coin and it lands on its side.

And the TARDIS trying to do what's best for him, as always.

I can't wait to see where you go with this. :)