Richard and Vickie Allen of Highland, Calif., lost custody of the boy, whom they are trying to adopt, after Allen was accused last week of molesting two family baby sitters. Allen, 49, pleaded innocent.
On Tuesday, the Arkansas judge who had approved the British couple's adoption of the little girls nullified his decision, saying the adoption was obtained fraudulently.
Until Wednesday, the Allens had been battling Alan and Judith Kilshaw of Britain for custody of the girls, who had been put up for adoption over the Internet.
Richard Allen said in a telephone interview Wednesday that he and his wife will no longer fight for the twins.
"We would have loved to be able to have been considered as adopted parents of the girls," Allen said. "But with all the matters that are going on here, it would be inappropriate for us to put too much effort into that."
The Allens cared for the babies for a month and a half last fall when the girls' birth mother, Tranda Wecker, retrieved them and had them adopted by the Kilshaws in Arkansas.
"Miss Wecker committed fraud and intentionally misled and deceived a number of people," Pierce said Wednesday. "It is my belief that she misled two attorneys and I really personally believe she misled the Kilshaws."
The judge said Wecker had signed statements and told several attorneys that she lived with an aunt in Arkansas. Under Arkansas adoption law, one set of parents involved in the adoption must live in the state for at least 30 days. Wecker, who lives in St. Louis, later admitted lying about her residency.
He said, however, Wecker did not lie under oath and did not sign a sworn statement that would make her subject to criminal penalties.
In response to Pierce's comments, Wecker's attorney, Gloria Allred, said she was shocked that the judge would call Wecker deceptive and denied that her client committed fraud.
"In his ruling he does not refer to any court documents in which Miss Wecker states she lived in Arkansas," Allred said. "If he's got evidence of that, then that should be available to us."
Pierce urged British authorities to return the twins to the United States for further proceedings on who should get custody. British officials said they will consider his ruling.
The Kilshaws said they will appeal the judge's ruling.
The Allens said they paid an Internet adoption service $6,000 for the right to adopt the girls. The Kilshaws said they paid $12,000.
Wecker has said she wants the twins back, and the girls' father, Aaron Wecker, said he wants the girls with him.