Kevin Costner Claims Estranged Wife Christine 'Grasps at Straws' as He Requests She Move Out by July 13

Costner is also alleging that Christine charged more than $100,000 to a credit card he has since canceled

Kevin Costner wants his wife Christine Baumgartner out of his California home by mid-July.

In court documents filed June 30 and obtained by PEOPLE, the Oscar-winning actor’s legal team says Baumgartner “grasps at straws with one baseless argument after another,” as to why she should be allowed to stay.

Costner, the document continues, “respectfully requests that Christine be ordered to vacate his separate property residence forthwith and no later than July 13, 2023.”

Related: A Complete Timeline of Kevin Costner and Christine Baumgartner's Divorce

Baumgartner has remained in the Santa Barbara compound, worth an estimated $145 million, since filing for divorce on May 1, despite a clause in her prenuptial agreement that he claims requires her to leave within 30 days. That deadline has since passed.

These latest documents from Costner, who bought the property in 1988 before he wed Baumgartner, come in response to his estranged wife's own June 28 filing, in which she stated his claims that she will not vacate the home are “simply not true” and that she will move out of their beachfront property by Aug. 31 if a child support agreement has been made.

The exes share three children together — Cayden, 16, Hayes, 14, and Grace, 13 — who have lived in the Santa Barbara compound their whole lives. In order to set up a "suitable separate household," for them, she has requested $248,000 per month in child support, a number Costner has rejected as "inflated."

On May 2, a rep for Costner, 68, confirmed to PEOPLE that Baumgartner, 49, had filed for divorce after 18 years of marriage. She listed their date of separation as April 11 and cited “irreconcilable differences,” requesting joint custody of their three children.

Since then, the separated couple’s legal teams have traded sharply-worded legal filings, battling over many issues, including child support.

Under the terms of their prenuptial agreement, Baumgartner is entitled to just $1.4 million, a sum Costner claims he has paid.

In their new reply memorandum, Costner’s attorneys mentioned local real estate listings, providing evidence that there are homes nearby that the former handbag designer cannot claim are unaffordable.

“Christine can afford to move,” reads their reply. “She has at her disposal almost $1,500,000 in cash to find alternative housing. Multiple 4-bedroom, 4-bathroom lovely homes are presently available, located in close proximity to Kevin’s separate property residence… Kevin made multiple offers to assist her in relocating.”

A source close to Costner recently told PEOPLE, “This is all about Christine. Kevin has gone above and beyond in providing Christine the necessary means to find a suitable place for her to move."

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In late June, court documents obtained by TMZ stated that Costner was willing to give Baumgartner $10,000 to cover moving expenses plus $30,000 per month toward a rental home.

In a declaration directly from Costner, the new reply memorandum confirms he paid Baumgartner those amounts plus the $1 million due under their prenuptial agreement.

“I offered her the full use of household staff to assist in making the move, and I offered to pay her now the additional $200,000 I owe her under the PMA in cash, rather than as a down-payment towards her purchase of a home... I also told her that I would continue to pay 100% of the children’s expenses since she filed for divorce, and I have done so.”

He added that “there are multiple very nice homes in the Santa Barbara area advertised for six-week and more rentals through Airbnb. She could have arranged for a month or two month or shorter term rental.”

Costner then detailed the effect this conflict has had on his upcoming screen project, Horizon: An American Saga, on which he serves as producer, director, writer and actor.

Because Baumgartner, Costner alleged, refused to vacate their home within 30 days of the divorce filing, saying she “did not respond by June 23 to my request that she at least move out of the primary bedroom,” he is now unable “to begin post-production work on Horizon.”

“Because I am not now comfortable sharing a residence with Christine, I very reluctantly changed my travel plans and delayed returning home,” said Costner, who allegedly went to his 160-acre ranch in Aspen, Colorado instead.

“This forced change in my plans is materially interfering with my work commitments,” he added of what he hopes will be “a four-movie project.” The first installment of Horizon, per the new document, is being planned “to show at film festivals later this year, with a theatrical release by year end.”

Costner also mentioned that because he is no longer involved in the hit Paramount Network series Yellowstone, the actor’s largest source of revenue, his “income going forward depends on timely completing and releasing Horizon films, starting with Horizon I.”

Attorneys for Baumgartner did not immediately respond to PEOPLE's requests for comment.

Costner further claimed that he canceled one of Baumgartner's credit cards because, throughout May and early June, she allegedly charged more than $100,000: “Christine began charging large sums on the credit cards payable to her divorce attorneys and forensic accountants. She gave me no advance warning each time she did so."

Costner and Baumgartner are due in court on July 5 for a case-management conference.

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