Good luck. I spent 10 years in the USAF and do not regret it. From what I recall, NOBODY was pushed to "give up custody of their kids" as a single parent. But make no mistake, you will be required at least these things:
A will. (well not required, but you are pressed to do this, even in the mobility line as you deploy, there is a JAG representative to help people make out a will before they go).
A medical/child care power of attorney, which goes with the below, really:
A Dependent Care form. This is a formal document, naming designated person(s), *who are NOT in the military*, who will care for your child in the event you deploy or become unable to care for your child due to military duty, in writing. And you will be held to it, believe me. This person would be able to, at a moment's notice, drop everything and take your child into his/her care and be a sort of surrogate parent in your absence, as needed. It would also require you name an interim person, if the designated party lives too far to take immediate temporary custody of your child----e.g. a daycare provider or friend who will care for this child until the other person is able to arrive to take over.
Hope this helps. Like I said, a recruiter can fill you in; read the fine print!