Twelve days after two young Iowa cousins vanished, the mother of one of the girls is asking authorities -- and her family -- to move on from their focus on her.

Misty Cook-Morrissey said a state agent asked during Monday's polygraph whether she had anything to do with the abduction of her daughter, 10-year-old Lyric Cook-Morrissey, and niece, 8-year-old Elizabeth Collins. She said she was asked whether she knows where they are and if she could take investigators to them, adding she answered "no" to all those questions.

The polygraph was the second test authorities had her take.

"It went well," Cook-Morrissey told The Associated Press in a phone interview. "They can rule me out of their book and move on to something else."

The polygraph came a week after authorities said Cook-Morrissey and her husband weren't cooperating. In a news briefing on Monday, Black Hawk County Chief Deputy Rick Abben declined comment on Cook-Morrissey's polygraph test but said investigators were getting better cooperation from her and her husband. 

The girls were last seen heading out on a bike ride on July 13 in Evansdale, a town of 4,700 in northeast Iowa. After combing the area and draining a nearby lake, authorities announced they felt the disappearance was an abduction, and said on Saturday they thought the girls were still alive.

Both Cook-Morrissey and her husband have spent time in prison on drug charges, NBC's John Yang reported Tuesday on TODAY, but Cook-Morrissey she said that had nothing to do with the girls' disappearance.

Elizabeth's mom, Heather Collins, said her relationship with her sister, Cook-Morrissey, has been splintering amid investigators' recent statements that Cook-Morrissey wasn't fully cooperative.

"Even though we would like to be as one family, it has made it to be two separate families," Heather Collins said of her sister, Misty, Lyric's mom.

There is a $50,000 reward for the girls' safe return. FBI spokeswoman Sandy Breault said Monday that investigators want to interview a person who was paddleboating on the lake around the time the girls disappeared. She said that person, who has not voluntarily come forward, could help investigators learn what happened to the girls but was not considered a suspect.

The Associated Press contributed to this report.

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The families of two missing Iowa girls said Tuesday they fear the girls may have been abducted, even as authorities continued to drain a lake in hopes of finding them. 

Elizabeth Collins, 8, and Lyric Cook, 10, left their grandmother's house in Evansdale, Iowa, for a bike ride last Friday afternoon around 12:15 p.m. Their bikes and one of their purses were found later Friday along a nature trail by Meyers Lake, on the outskirts of town, but the girls had vanished, NBC's Kevin Tibbles reported.

Hundreds of volunteers pored through cornfields and officials searched the area by land and air, but no clues were found. Officials started draining the lake on Monday.

"It is our opinion that we should be 100 percent sure, and in order to be 100 percent sure, we're going to have to drain that lake," Captain Rick Abben of the Black Hawk County Sheriff's Office said at a press conference Monday.

It could take two full days to drain the lake, NBC reported. Drought conditions may assist with emptying it faster. The Black Hawk County Sheriff's Office did not immediately return a phone call from NBCNews.com on Tuesday morning.

On Monday night, Evansdale residents packed a local church to hold a vigil.

"It's very difficult, but we're trusting in the Lord and just trying to be patient and let everybody do their job, and we're doing a lot of praying," Misty Cook-Morrissey, Lyric's mother, told reporters.

There's no evidence of foul play, and family members have been cooperative, officials said, reported KWWL.com in Iowa.

"I have hope because of the Lord's great love," Heather Collins, Elizabeth's mother, said at the vigil.

Fears of kidnapping
On Tuesday, Collins told ABC News' "Good Morning America" she believed the girls had been kidnapped, and asked for their safe return.

"I want to say to them that my husband and I have forgiven them," she said. "God has forgiven them already. So we have forgiven them and we just want our children back safe and sound. That's all we want. We don't even want to know who the person is."

Wylma Cook, the girls' grandmother, added, "Whoever has them, just turn them in, let them loose anywhere so they can call me. Lyric knows my cell phone, she knows my house phone."

Evansdale, a town of 4,500, is located in northeastern Iowa, about 100 miles northeast of Des Moines.

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