The woman accused of kidnapping her children from their Lakeville father had recently been upset about her custody situation, according to court documents, and had allegedly told a family member that she struggled to resist driving into an oncoming truck.

Valerie McGrath, 47, was ordered held on $50,000 bail Tuesday in Wareham District Court. She pleaded not guilty to two counts each of reckless endangerment of a child and kidnapping of a minor by a relative, Plymouth County prosecutors said.

State Police arrested McGrath in Raynham on Monday after a search that began a day earlier, when she allegedly picked her children up with the permission of their father — who has sole custody — but did not return with them at the scheduled time.

When they were found, police said, the children were in good health. They were returned to the custody of their father.

But while the children were missing, police had said in a statement that because of “the actions and statements made by [Valerie] McGrath in the last few weeks, the Police Department has concerns for the safety of the children.’’

According to an incident report filed in court, police spoke to one of McGrath’s sisters, who said the suspect had previously made alarming statements about the custody situation surrounding her children.

McGrath had allegedly told her sister that she did not want to return her children to their father. Another family member had told police McGrath had not seen the children in six weeks.

“It’s taking every fiber in my body not to drive into this oncoming truck,’’ McGrath said, according to her sister’s statements in the police document. She also allegedly told her sister that she expected there to be an Amber Alert next time she had her children.

No Amber Alert was ultimately issued, though Lakeville police made a feverish social media push to alert the public to the search.

In a statement, State Police spokesman David Procopio said the agency considered the use of an Amber Alert, but determined that there wasn’t enough information to demonstrate that the children were in harm’s way.

McGrath’s conversation with her sister was weeks before the alleged abduction, he noted, adding that State Police were investigating the case vigorously even without issuing an alert.

“We had eyewitnesses and a video security tape that showed the mother and the children,’’ he said. “The witnesses said the children appeared fine, and investigators’ observation of the security footage indicates the same thing.’’

The delicate consideration required to use Amber Alerts properly was on display in October, when authorities issued an Amber alert for a woman who had taken her ailing infant son from a Pennsylvania clinic to Boston Children’s Hospital.

Family members and an attorney for that woman, Tiffany Cherry, protested that the alert was an overreaction, and that she thought she could get the best care for her child here. State Police said at the time there was “an indisputable concern for the little boy’s well-being.’’

In McGrath’s case, an attorney could not be reached for comment. She is due to return to court Jan. 20.

Travis Andersen of the Globe staff contributed to this report. Andy Rosen can be reached at andrew.rosen@globe.com. Follow him on Twitter @andyrosen.