Terrified Corby and East Northamptonshire MP Louise Mensch was asked to choose which of her children should die by an internet user.
Frank Zimmerman, 60, an agoraphobic living in a run-down house in Spinney Road, Gloucester, was convicted of sending by public communication network an offensive, indecent, obscene, menacing message or matter in his absence on Tuesday.
In a victim impact statement read to the court Mrs Mensch said: “I was terrified on behalf of my children.
“I was in New York with my husband recovering from an operation and my children were with their father and to receive a threat like this made me very upset
“I was 3,000 miles away from my children and I was worried for their safety and the safety of my ex-husband.
“I felt powerless to do anything.”
Speaking on Twitter after the case on Tuesaday, Mrs Mensch thanked everyone for their support.
She said: “Thank you everybody for the kind words re: troll.
“You don’t know who is making anonymous threats.
“So you always have to worry. Beyond that I will not comment until after sentencing (police advice).
“However I do want to record my thanks to all police who worked on this case and will do so in more detail when permitted to.”
The sinister email was purportedly sent from the online hacking group Anonymous, Gloucester Magistrates’ Court heard.
But police later charged Zimmerman, who has failed to attend any court appearance to answer the single charge he faced or give proper instructions to his solicitor, blaming his agoraphobia and depression.
District Judge Brown decided to proceed with the case in Gloucester without him on Tuesday.
Gaon Hart, prosecuting, told the court that Zimmerman sent the email to Mrs Mensch after she spoke out publicly during last summer’s riots, calling for the police to be able to temporarily close down social network sites, such as Twitter and Facebook, if necessary.
Zimmerman originally made contact with the MP on Twitter using the pseudonym Tim Cavendish.
He claimed he had information about Piers Morgan and the telephone hacking scandal engulfing the News of the World, the court heard.
Mrs Mensch sent him her personal email address and it was to that account that Zimmerman sent the threatening message.
The email, which was timed at 10.47pm on August 22, said: “Which kid is to go?”
Mrs Mensch took the threats seriously and immediately contacted the police.
Zimmerman first became a suspect for threatening Mrs Mensch when Independent newspaper columnist Terence Blacker, who was a former neighbour of the defendant in London, received a similar email.
Zimmerman is on unconditional bail until he is sentenced on Tuesday, May 8.