I will answer this question based upon the law of the jurisdiction where I practice family law (Utah).
So the question is: How can I get an emergency hearing for custody and child support?
The answer: Have a good reason.
A very good reason. A reason that would justify asking the court to address the issue on an emergency basis.
Do such reasons exist? Yes. Are such good reasons easy to establish? Generally, no, unless one tries to obtain emergency child custody through a protective order proceeding (more on why below).
Is it easy to lie about having good reasons for an emergency child custody order and obtain an emergency child custody order under false pretenses? Yes, especially if one tries to obtain emergency child custody through a protective order proceeding (more on why below).
Here are some ways to obtain an order of child custody (and possibly for child support too) in not particular order (with links to the statutes that govern them):
1. By protective order.
—Cohabitant Abuse Act protective order
2. Divorce or parentage action
—motion for TRO (ex parte motion for child custody (and child support))
6. Termination of parental rights action
Utah Family Law, LC | divorceutah.com | 801-466-9277