Protective orders DO provide certain protections, including no contact with the children, financial support provisions, and they enable the police to make an arrest at the first contact, before it escalates.
The federal firearms provision at issue in the court opinion requires a conviction of a misdemeanor crime involving the use of force against someone in a specified domestic relationship to the offender. There is a separate federal provision that bars individuals subject to permanent (not temporary) protective orders from possessing firearms (which can be another advantage to obtaining an order).
What is safest to do in a particular situation is very fact-sensitive, so it is best to contact an advocate for guidance--preferably at the local women's shelter, the prosecutor's office, or at the National Domestic Violence Hotline. Even if you conclude it's safer not to leave (yet), an advocate can help with safety planning to reduce the risk to yourself and your children (and pets).