Short answer. Yes. There is a petition for judicial authority to administer or encumber specific separate property of the abandoning spouse and to use the fruits or proceeds for the family's support, and it is governed by the same summary rules — so it is meant to move quickly.
What the law says
The petition for judicial authority to administer or encumber specific separate property of the abandoning spouse and to use the fruits or proceeds thereof for the support of the family shall also be governed by these rules.
Family Code, Article 248 — Petition to Administer the Abandoning Spouse's Property. Read the full provision →
Reaching property that is not yours
What makes this remedy unusual is that the target is the abandoning spouse's separate property — property that is his alone, not part of the community or partnership. Ordinarily a spouse has no power over it at all. The article opens a door to it, and the reason is the family's support: the obligation to support does not lapse because the person owing it has left, and the law is not willing to let a family go without while assets sit idle in the name of the one who walked out.
Specific property, and for a stated purpose
The wording is tight in two ways. The property must be specific — you are asking about identified assets, not for a general power over everything he owns. And the authority sought is to administer or encumber it and to use the fruits or proceeds thereof for the support of the family. That is what the money is for; the petition is not a way to recover past debts or to settle scores between the spouses, and any damages claim between you is in any case a matter for a separate action.
It rides on the summary rules
The phrase shall also be governed by these rules attaches this petition to the same title as the other summary proceedings, with everything that implies. The judge conducts the preliminary conference personally, without counsel assisting; if the petition survives that conference it is decided in a summary hearing on affidavits, documents or specified testimony; if your spouse cannot be brought in despite all efforts the court may proceed ex parte while endeavouring to protect his interests; and the judgment is immediately final and executory.
What the petition has to establish
Three things carry it. The abandonment — when he left, what has been provided since, and what efforts were made to reach him. The property — identified precisely, with the title or records showing it is his separate property, together with what it earns or could earn. And the need — who is being supported, and what their support actually costs. Assemble those, along with the record of your attempts at notice, before consulting a lawyer; the notice problem is usually the part that determines how fast this moves.