Each state has different laws. Some states have a presumption to allow the move, some not to allow the move, and some follow what is in the best interest of the child standards with no presumption. What state do you live in?
After two court battles and spending about $15,000 on our side(I think she spent about $30,000)BM moved 3,000 miles away with then 10 year old SD.
We get the summer starting 2 days after school lets out until 2 weeks until summer begins, every spring break, all winter break in even years 1/2 in odd, and Thanksgiving break anytime we want to pay all the travel costs ourselves.
We split the travel expenses in the same % as the child support order (as dictated by WA law, but WA is the only stat that I know that mandates this). Some judges make the moving party pay the travel expenses as they are the ones creating the expense (this is the way I think it should be).
With small children they also have to be escorted on airplanes each way making it 3 round trip tickets instead of 1. After age 5 on direct flights they can fly as unaccompanied minors for an additional $75 fee each way.
It is difficult to have a long distance relationship with your children, especially before they can really start using the computers and phones on their own.
Document everything at this point that the mother says about her intent to move in order to interfere with the relationship between the child and the father. That kind of information can make a big difference in a court battle in a state that does not have a presumption to allow the move.
Good luck.