One CANNOT reaadopt a child one has not already adopted. I can't imaginr any way to do a Finalization of a Child Adopted Internationally with a party not already part of the international adoption. The international adoption set out multiple requirements that had to be complied with for this adoption to occur, and your new spouse was not part of that process.
You likely need to complete your readoption in accordance with CA statute and then do a step parent adoption. Here is a reference:
http://www.childwelfare.gov/systemwide/laws_policies/statutes/intercountryall.pdf
Search CAL. FAM. CODE § 8919 : California Code - Section 8919
(a)Each state resident who adopts a child through an intercountry adoption that is finalized in a foreign country shall readopt the child in this state if it is required by the Department of Homeland Security. Except as provided in subdivision (c), the readoption shall include, but is not limited to, at least one postplacement in-home visit, the filing of the adoption petition, the intercountry adoption court report, accounting reports, the home study report, and the final adoption order. If the adoptive parents have already completed a home study as part of their adoption process, a copy of that study shall be submitted in lieu of a second home study. No readoption order shall be granted unless the court receives a copy of the home study report previously completed for the international finalized adoption by an adoption agency authorized to provide intercountry adoption services pursuant to Section 8900. The court shall consider the postplacement visit or visits and the previously completed home study when deciding whether to grant or deny the petition for readoption.
(b)Each state resident who adopts a child through an intercountry adoption that is finalized in a foreign country may readopt the child in this state. Except as provided in subdivision (c), the readoption shall meet the standards described in subdivision (a).
(c)(1)A state resident who adopts a child through an intercountry adoption that is finalized in a foreign country with adoption standards that meet or exceed those of this state, as certified by the State Department of Social Services, may readopt the child in this state according to this subdivision. The readoption shall include one postplacement in-home visit and the final adoption order.
(2)The petition to readopt may be granted if all of the following apply:
(A)The adoption was finalized in accordance with the laws of the foreign country.
(B)The resident has filed with the petition a copy of both of the following:
(i)The decree, order, or certificate of adoption that evidences finalization of the adoption in the foreign country.
(ii)The child's birth certificate and visa.
(C)A certified translation is included of all documents described in this paragraph that are not in English.
(3)If the court denies a petition for readoption, the court shall summarize its reasons for the denial on the record.
(d)The State Department of Social Services shall certify whether the adoption standards in the following countries meet or exceed those of this state:
(1)China
(2)Guatemala
(3)Kazakhstan
(4)Russia
(5)South Korea
(e)In addition to the requirement or option of the readoption process set forth in this section, each state resident who adopts a child through an intercountry adoption which is finalized in a foreign country may obtain a birth certificate in the State of California in accordance with the provisions of Section 102635 or 103450 of the Health and Safety Code.
CAL. FAM. CODE § 8900 : California Code - Section 8900