Kevin Costner's Estranged Wife Christine Tears Up on the Stand During Child Custody Hearing Appearance

Costner and his estranged wife are locked in a contentious fight over child support amid their bitter divorce.

Kevin Costner and his estranged wife appeared in a Santa Barbara, California courtroom on Thursday for a hearing over contested child support, and the showdown proved to be an emotional setting.

Christine Baumgartner took the stand and choked back tears when questioning shifted from the Yellowstone star's beach club estate to his expansive ranch in Aspen, Colorado, where the kids have vacationed on numerous occasions and consider the estate a special place. An eyewitness tells ET that Baumgartner "started tearing up and reached for a tissue" when that portion of the questioning began. A 30-second pause ensued before the judge called for a five-minute break.

Costner and Baumgartner are in court to settle their bitter dispute over how much Costner should have to fork over in monthly child support for their three children -- sons Cayden, 16, and Hayes, 14, and daughter Grace, 13. The court has temporarily ordered Costner to pay her $129,000 per month (he wanted to pay $51,900), and she recently went to court requesting that the amount be increased to $175,000 per month (she initially wanted $248,000 per month). Baumgartner filed for divorce in May after 18 years of marriage.

The 68-year-old actor wore a beige suit and black tie and, according to the eyewitness, he seemed relaxed at the hearing. His demeanor, however, changed when Baumgartner's attorney stated in court that Costner had more than enough money to pay for both of their legal bills, a point of contention as of late.

"He seemed irritated when Christine's attorney said that he should pay for both attorney fees," the eyewitness said. "He visibly shook his head when the lawyer said he could afford to pay for both."

The eyewitness went on to say Costner didn't shy away from looking at Baumgartner, 49, before she took the stand.

"He would sip his water and he would look at her," the eyewitness said. "He was not averting his gaze."

At the hearing, Baumgartner testified it was important for the kids to have a "comparable lifestyle" to the one they enjoyed when she and Costner were still a couple, thus her request that the court increase the amount Costner should pay her in monthly child support. She testified that the children love the beach club estate and that they're "home in the water."

But ahead of the hearing, Costner's legal team on Wednesday afternoon filed new court documents in which he blasted Baumgartner's claim that he "steadfastly refuses" to pay child support sufficient to meet the children's reasonable needs.

In the court documents obtained by ET, Costner called Baumgartner's claim "demonstrably false and purposely inflammatory," while insisting that Costner and Baumgartner "simply differ on what 'reasonable needs' means in the context of child support." Costner also didn't mince words when describing her "baseless character attacks" on him.

"Christine's relentless 'jihad' against Kevin's character adds a level of animosity to this proceeding that is wholly unnecessary," the court documents state.

In those same court documents, Costner claimed Baumgartner has a "boyfriend" -- a notion she later refuted -- and that the boyfriend "recently gave her $20,000."

While on the stand at Thursday's hearing, Baumgartner was asked about her Hawaii vacation in July with her and Costner's mutual friend, Josh Connor. Baumgartner was asked if Connor was her boyfriend and she said, "No." Baumgartner, however, did concede Connor gifted her $20,000. She was emotional on the stand and wiping away tears as she disclosed giving half of the money to her mother. When asked why she was being emotional, Baumgartner said she's concerned with her mother's wellbeing. She also stated that, during the marriage, Costner gave her mother $5,000 monthly, which she said her mother is no longer receiving.

As for Baumgartner's claim that the kids are "home in the water" and therefore needs more in child support in order to provide a "comparable lifestyle" like the one they enjoyed at Costner's ocean-front beach club estate, the actor states Baumgartner already leased a full acre, four-bedroom house in nearby Montecito that's only "4 minutes from the beach (5 minutes by bicycle)." Costner also stated Baumgartner's Montecito house -- a six-month lease for $40,000 -- also has a larger pool than the one at his beach club estate.

He concluded in his court docs that "the reasonable needs of the children are fully met by a child support order of $63,209 per month" and that "support greater than that amount is simply disguised spousal support." He added, "Christine will have her opportunity to convince the Court that she is entitled to spousal support, but that is not the issue at hand for this hearing."

Costner and Baumgartner have a second child custody hearing set for Friday.