Actor Kevin Costner’s divorce from Christine Baumgartner is threatening to take a nasty turn, as an almighty dispute builds about their shared home.

Baumgartner, 49, filed for divorce from the 68-year-old Yellowstone actor on May 1, citing irreconcilable differences after 18 years of marriage.

Costner was reportedly blindsided by her decision.

“It is with great sadness that circumstances beyond his control have transpired which have resulted in Mr Costner having to participate in a dissolution of marriage action,” one of the star’s representatives said.

“We ask that his, Christine’s and their children’s privacy be respected as they navigate this difficult time.”

The Bodyguard star Costner and Baumgartner have three children together: Cayden, 16, Hayes, 14, and Grace, 13.

But while Baumgartner, a handbag designer, was spotted out and about in Santa Barbara on Tuesday (local time), the estranged couple’s problems are reportedly escalating – as she refuses to leave the $US145 million ($214 million) home they shared in southern California.

Court documents filed by the actor and director accuse Baumgartner of refusing to move out within 30 days of filing for divorce, in defiance of the couple’s prenuptial agreement. According to the documents, she says she won’t move until Costner agrees to various financial demands.

Costner’s lawyers said he has given her more than $US1.2 million ($1.8 million) to relocate. There have also been other payments, bringing the total to about $US1.45 million ($2.1 million).

“Securing his right to access his separate property residences in the event of a divorce was an important priority for Kevin,” the lawyers said.

“Kevin was married once before and, upon separation, he found himself without a home base and unable to live in his own home. He never wanted that to happen again.”

But her lawyers fired back, saying Costner “seeks to kick Christine and their three children out of the house that the children have lived in for their entire lives”.

“Although the legal basis for Kevin’s request to kick his wife and children out of their home is all but nonexistent, this is still a matter of critical importance for Christine,” Baumgartner’s lawyer John Rydell reportedly said in the documents.

A Costner source told People magazine it was “disingenuous to bring the kids into this”.

“This has nothing to do with the kids. The kids’ foundation is solid. This is all about Christine,” they said.

“Kevin has gone above and beyond in providing Christine the necessary means to find a suitable place for her to move.”

TMZ reported that Costner claims to own all three of his properties, and none jointly with Baumgartner.

Costner also has four other children from prior relationships. TMZ reports he is seeking “joint custody” of his children with Baumgartner.

A day after their split was revealed, Page Six reported Costner was “stunned” by her decision to end their marriage.

“There was no issue of cheating at all,” a source told the publication.

“Kevin was very surprised by Christine’s actions; he obviously doesn’t want the divorce and he would take her back. It’s disappointing, he loves her and he loves his children.”

Elsewhere, a source told People that the divorce was not Costner’s idea.

“It was not anything that he wanted or sought, and if he could change the situation, he would,” they said.

Costner and Baumgartner married in 2004, about a decade after he split from first wife Cindy Costner, 66.

The property dispute will be heard by a Californian court on July 5.