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Yes you can. I am confused on where you are now and where the original order was heard. If you can tell me where the original order was issued from I can send you the information you need to file.
As far as your moving, if you have full custody you can move without the courts permission, but if it is joint custody if you leave the state without telling the non-custodial parent or without their consent you can be charged with custodial interference or kidnapping. In your situation as it is now that would not happen since it is what the father wants anyway.
Ok....I was under the impression you were moving to South Carolina....nevermind that ;-)
You will want to petition the court for a modification hearing to be able to move & live in California with the girls, correct? Now, just so you know this is probably going to be a costly agreement for you to make with the court because if you are choosing to live in California you will normally have to be willing to pay the costs of getting the girls to their father for visitations...that would mean you would have to pay for airfare or whatever travel to get them there and back to you.
As far as HOW to petition the court or what to file, you will file for a modification of custody hearing. This will give you and their father the opportunity to speak with the court and ask that the court rule on where the children can live, who will have full, joint, or legal custody, what child support will be paid, if any, and what will be paid for transportation, etc. To do this, you will file in the South Carolina courts but I am not finding this form available online. I suggest contacting the Clerk of Court for that county HERE to see if they have these available in their office.