After 10 years of sharing custody of their son, Ry­der, Kate Hudson and her ex-hus­band, Chris Robinson, have been involved in a nasty custody dispute.

In Touch can exclusively reveal that Chris wants full custody and a big child support payment from Kate.

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“When they finalized their divorce [in 2007], they agreed to joint custo­dy. Chris now wants full custody of Ryder,” says the insider. “This has been an ongo­ing issue for months now, and they are still battling it out behind closed doors.”

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While it’s a highly unusual step for a couple whose divorce was finalized so long ago, the pair has hired lawyers who specialize in cus­tody cases and, as court papers published in the new issue of In Touch reveal, Kate, 37, and the Black Crowes front man, 50, even hired a $500-an-hour private judge to handle their case last June.

“Chris and Kate have disagreed over her parenting style. He’s worried that Kate hasn’t been as hands-on as she should be, and he wants more guidance over their son,” the insider explains. “He’s seeking a hefty child support payment to go along with full custody.”

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“Chris tours as much as Kate travels for work, so they’ve shared equal custody for as long as they’ve been divorced and it has never been a problem,” the source adds. “In fact, Chris didn’t want anything from Kate, especially money-wise, when they originally settled. But it’s sud­denly become a different situation.”

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“Kate isn’t giving up on the agreement she and Chris settled on in the first place,” says the insider. “She believes this is all about money.”

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