-"full custody" (pretty much impossible these days)
-mother making all parenting decisions
-father being the only one to travel, especially if the mother is the one moving away
-Christmas and birthdays being spent only with the mother (they will likely alternate)
-full legal rights? Nuh-uh.
-who W spends time with when with her father? None of the mothers concern. Trust me I tried very hard with this one regarding my own children, even when some of the people I was concerned about had a criminal record. As long as there are no safety concerns between father and child, there is nothing you can do about other people being around.
- As for the 'in case of the mothers death' one, you need to write a will, but at the end of the day if the father has been active in the child's life, he can contest the will anyway.
Good luck OP but if the father decided he wants involvement, I think you are going to need to review your wishes and change them to more realistic ones.