what paperwork do i need to authorize the judge to order my spouse to pay for my attorney or for the judge to order a public defender?

You need to file a motion with the court to request attorney’s fees from the other party.
Family court is not criminal court. It is a civil issue. You are only get a public defender in criminal cases.

Get a lawyer before you screw everything up. The court does not take legal ignorance as an excuse

In a civil case you may not have that right.
The defendant does not have to make use the plaintiff can mount a case against him.

If this is a civil matter there is no access to public defenders, they only serve on criminal cases. If you're divorcing you can include the request that your spouse pay for your lawyer. If you're suing your spouse civilly you can include language that he/she has to pay in the case they lose. But assuming you're married and facing some civil case that doesn't qualify for a PD, no judge is going to force your spouse to pay your legal costs.

ask your attorney. in most states, your spouse is NOT obligated to defend you in court or pay the attorneys to do so -- that's your problem

Get a lawyer. Maybe I need to explain.

I assume we're talking about divorce. You get a lawyer, and then the lawyer knows how to fill out paper work for that. The lawyer can also tell you if it's possible.

A public defender is for a criminal trial. Not a civil case. Call your local bar association or legal aid group.

What is the case about?

If your spouse can afford it you won't be getting a public defender.