You would have the right to request a annulment based on her lies about her finical situation as well as her legal problems. The good news is if it is just the legal situation you are concerned about, since she married out of state the courts will likely approve her to take the child out of state.
If you are interested in filing for a annulment you would need to do so in the state of California since you are a resident there and the marriage took place there.
Marriage under California law is a personal relation arising out of a civil contract between a man and a woman, to which the consent of the parties capable of making that contract is necessary. But the parties' consent does not alone constitute a marriage. To validate the marriage, the consent must be followed by issuance of a license solemnization and authentication and the certificate of registry of marriage shall be returned.
Either party's consent to the marriage or domestic partnership was obtained by "fraud," unless the defrauded party thereafter, and with full knowledge of the facts constituting the fraud,
The type of "fraud" sufficient to support a judgment of nullity must go to the very essence of the marital [or domestic partnership] relation. Thus, fraud or deceit sufficient to avoid an ordinary contract will not necessarily warrant a judgment of nullity. The alleged misrepresentation or concealment must have been vital to the relationship, directly affecting the purpose of the deceived party in consenting to the marriage/domestic partnership.
I would strongly recommend that you seek legal counsel in your area to discuss wither you have a good case for annulment and if not discuss the implications of a divorce in these matters.
I wish you the best in the new year.