You can ask the court for sole legal and physical custody. You will have to give notice to the bio-dad but there are ways to do this even when you don't know where he lives. And you may want to look at adoption of them by your husband later on. I suggest you get some legal advice about your specific circumstances.
Absent a court order stating otherwise, you can take your children out of the country for vacation. If you want a court order, then file for custody. You will have to serve Dad with papers. You may also want to consider having your current husband adopt your children. http://www.courts.ca.gov/1185.htm
Consult with an attorney to assist with the process and provide legal representation to achieve your custody goals. Since you have provided for your two children solely, the court would likely order the your family situation remain undisturbed.
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