Excellent, excellent, excellent....you've covered all the bases. I told you that you were articulate! I'm so proud of you. Wish you were my granddaughter! The letter could go as is, but there is only one sentence you might want to take a look at.

"If I haven’t changed your mind yet because you don’t want to do this for me, would you please do it for my dad? "

I think instead I would say something like:

"There is even a more important reason, however that I am making this request. It's my dad."

I also agree with the suggestion Freckles had. These are all minor points; however, and no two people are ever going to say the same thing the same way. You have done it Bridget! Whether you win him over or not, you have made the effort to do a good thing. Yes you are taking a risk, a risk of more rejection, doing a good thing is not often easy, but it is something you can feel proud of.