The new Amber Valley MP, Nigel Mills, used his maiden Commons speech to back an inquiry into how police dealt with a mentally-ill killer.
Rachael Slack and her 23-month-old son Auden were stabbed to death by her ex-partner, Andrew Cairns, in Holbrook last Wednesday. He then killed himself.
He had been detained twice in the previous week, and was on police bail.
The Independent Police Complaints Commission is investigating how police handled the case.
Mr Mills told MPs: "The case is made more difficult by the fact the alleged perpetrator of these offences had been arrested twice by the police the week before from accusations of domestic violence.
"[He'd] also been receiving help for mental illnesses.
"I do welcome the fact that Derbyshire Police has called in the Independent Police Complaints Commission to review their actions."
Miss Slack's mother Jean and brother Hayden said the family had been left devastated.
In a statement they said: "We were numb with shock when we were told of Rachael's death and that of her lovely son Auden."