S.J.
First and foremost, whatever you write make sure you are sincere. You don't want your feelings of irritation with your father coming out in the letter. Do you feel as if you can do that? If not, I wouldn't write the letter.
I guess it would help me to help you if I knew what excited you about this woman. Tell us your thoughts about why you are excited to welcome this person into your family. Just jotting your thoughts down here will help you.
A better idea might be a card - they make fantastic ones that say things we cannot come up with - they pay people to be brilliant with words!
If you decide to do it yourself, just keep it short and sweet -
" I want to welcome you to our family, we have a lot of love to give and I am excited for you to be a part of that. I look forward to getting to know you and your children better as the years go by. I wish you and my dad the best!"
I am no hallmark.....