My wife is originally from England and our daughter was born in the U.S. She threatens to take her and raise her in England all the time.
What are my rights to keep her and prevent my wife from taking her without my permission to England?
While I am not licensed to practice law in your state and cannot give you legal advice, I can give some general observations on this issue based on the jurisdiction where I practice.
If your daughter has a passport you should obtain possession of the same immediately, which will cause immediate problems if your wife actually does try to take them from the country.
Also, http://travel.state.gov/abduction/prevention/passportissuance/passportissuance_554.html has important information and steps you can take to combat potential international removal issues.
International custody issues are complex and there is no doubt that taking steps while your child is still in the country is your first and most effective line of defense.
Family law is based on statutes that are state specific. I am licensed to practice in Nebraska and am not able to give specific and detailed legal advice regarding your situation as you will likely need to file initial paperwork in your state. You need to contact an attorney licensed in your state who specializes in domestic litigation. Cordell & Cordell, PC has offices across the country and I highly advise you to contact one as soon as possible.