You are going to pursue the return of the funds she moved abroad, and that is going to be most readily done in family law court through a marital dissolution or through a legal separation filing - not in civil court with a tort claim. As will she with the cases she has filed have to serve you, you need to effect service of process on her. Depending on where she moved to, you need to effect service by the Hague Convention or by the Inter-American Convention. You are going to need to retain counsel.
Since this involves (apparently) large dollar amount there may be some significant legal implications under the Patriot Act. Some possible civil remedies exist if this is lot of money --remedies which might be more effective then family court. What works best depends on many factors, so on- line advice will not suffice. But yes, most of what you can do you can do in California--which does not mean these things will actually work. You can get orders all day long... but she could easily ignore them UNLESS you are in a position to obtain a prejudgement writ of attachment on property located here.
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As state above you should hire an attorney to help you with this matter because of the complexity of issues. You should also consult with an attorney in the country she is in.
Please note that this answer does not constitute legal advice, and should not be relied on, as each situation is fact specific, and it is not possible to evaluate a legal problem without a comprehensive consultation and review of all the facts and court pleadings filed in the case. This answer does not create an attorney-client relationship.
Based on what you have written, it does appear that California could take jurisdiction over your case. Therefore, to answer your question directly, yes you likely can proceed in California.
The devil is - as always - in the details, and so I suggest you contact an attorney to develop a workable strategy.