Custody Case in the UK to move to USA?

He can fight you removing his child from the country. If he does,only a judge can give you permission to take the child out of the country. For a judge to agree,you are going to have to submit a plan on how the child and her father are going to be able to spend time together. Most likely you will be responsible for any travel expenses several times a year for your child to visit her father. No judge is going to allow you to leave and deprive the father of his rights to his child.