A mother has been extradited to NSW and charged with attempted murder after she allegedly tried to drown her two sons in the Murray River, leaving one boy in hospital and police searching the water for the second.

The woman walked to the river in Moama, on the NSW-Victoria border, with her children and told her eldest son, aged nine, to get in the water before she held his head under, police told Bendigo Magistrates Court on Friday afternoon.

Detective Sergeant Trent Swinton told the court the younger son, aged five, was screaming during the incident.

The woman then allegedly turned to the younger son, while the older son managed to struggle free before he was attacked by a pit bull.