"Baby Veronica" adoptive parents Matt, Melanie Capobianco seek deal over custody

Updated at 5:36 p.m. ET

TULSA, Okla. A South Carolina couple seeking to adopt a young Cherokee girl took their fight to Oklahoma on Wednesday, hoping to visit the child who previously lived with them for 27 months and seek a compromise with her biological family that would return Veronica to their home.

Matt and Melanie Capobianco believe they have done everything necessary to regain custody of the girl, who is about to turn 4. The U.S. Supreme Court said in June that provisions of the Indian Child Welfare Act, which would favor the girl's father, didn't apply in the case, and a South Carolina court awarded the couple custody on July 31.

The ongoing dispute has raised questions about jurisdictions, tribal sovereignty and the federal law meant to help keep Native American tribes together.

"We made the trip to Oklahoma to get our daughter," Matt Capobianco said at a news conference in downtown Tulsa on Wednesday. "Veronica will be coming home, but if there is going to be some thoughtful solution that continues to involve all who love her, then this is the time."

The girl, under a Cherokee Nation court order, has been with the family of Dusten Brown, her biological father. The tribe's chief urged patience.

"The Capobiancos have requested the Cherokee Nation and Dusten Brown to follow the South Carolina court's order, but they forget that Dusten Brown has the same rights to have his arguments heard before our Oklahoma courts and Cherokee Nation Tribal Court," Chief Bill John Baker said. "The Cherokee people throughout time have stood our ground and for the rights of our people, and this is no different. We will continue to stand by Dusten and his biological daughter, Veronica, and for what is right."

Oklahoma Gov. Mary Fallin urged the families to get together and talk — even threatening Brown with extradition to South Carolina on a charge of custodial interference if he was "unwilling to cooperate."

Veronica was born in late 2009. Brown initially did not press his parental rights — the girl's mother is not Native American — but when he discovered Veronica was going to be adopted, he objected and said the ICWA favored the girl living with him and growing up learning tribal traditions.

The Capobiancos and their supporters said Wednesday a compromise is in order.

"We don't seek victory. What we seek is peace for our daughter," Melanie Capobianco said.

Troy Dunn, a family representative, said he was willing to meet with Brown to discuss arrangements.

"Only one side has been deemed the rightful parents," Troy Dunn said at the family's news conference. "Possession is not nine-tenths of the law."

A handful of protesters shouted "Keep Veronica home" and "You're trying to break laws in Oklahoma" at the Capobiancos as they emerged from a hotel after meeting with reporters. Some held signs reading "Keep Veronica Home" and others that were written in the Cherokee language.

Under the Indian Child Welfare Act, the Cherokee Nation has a vested interest in the child and, if invoked at the right time, the law allows the tribe to take over the adoption proceedings. In June, the U.S. Supreme Court ruled that South Carolina courts should decide who gets to adopt Veronica, rejecting earlier decisions in South Carolina that said the federal Indian Child Welfare Act favored her father.

South Carolina Gov. Nikki Haley has written to Oklahoma Gov. Mary Fallin seeking Brown's extradition after he was charged with custodial interference after missing a court hearing this month. Fallin initially said she would consider the warrant next month, after Brown's expected Oklahoma court appearance, but on Wednesday she tried to use the extradition papers as leverage in an effort to get the families talking.

A first step would appear to be setting up a meeting between the Capobiancos and Veronica.

"Mr. and Mrs. Capobianco deserve an opportunity to meet with their adopted daughter. They also deserve the chance to meet with Mr. Brown and put an end to this conflict," Fallin said.

The Oklahoma governor urged a quick resolution and said, "If Mr. Brown is unwilling to cooperate with these reasonable expectations, then I will be forced to expedite his extradition request and let the issue be settled in court."

Fallin did not set a deadline. The Capobiancos said they didn't know how long they planned to stay in Oklahoma.

Dunn said he would meet with Brown anywhere, anytime to develop a plan to raise the child.

"There is but one solution which takes Veronica's short-term and long-term needs into account: compromise," Dunn said.