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Yes, you can always modify the custody/visitation order - the judge will (hopefully) enter an order that's in the "best interests of the children."
The real benefit you have here is the ages of the children - 13 and 15. The judge would most likely ask them where they want to live and with whom.
Do you know what they want to do?
No, as long as they are you children - you can put them on your medical (at a price of course).
Well, to answer your question - can you get joint physical and legal custody in California? Absolutely yes.
Will you? That would depend probably on what the children want to do - they are old enough to know their mind and what they want. Hopefully they know what's in their best interest.
So, as such, if you and they can join together - then yes, absolutely I think you can get joint legal and physical custody of the children if you petition the court that they want to spend 50% of their time with you.
Most likely, I would think the mother would just consent rather than go through the hassle with the courts - especially if that's what the kids want - she should realize she's fighting a losing battle.