Im the opposite!
On the one im leasing, I get nervous!
But on other horses, im fine!
You just need to keep on thinking, Im the boss.
if you relax your body in the saddle, then you will begin to feel naturally relaxed.
Just imagen your dads horse is your TB.
Maybe create a bond on the ground, so you know he likes you and trusts you.
That could help alot,
when ever I ride someone elses horses, I have to do everything for that horse (not because they've told me to)
I tack them up, rug them, muck them out, groom etc.
This gives me an idea on what their like and just makes me feel safer.
Hope this helps a little