The wicked allegations were made after the former BBC Countryfile presenter happily agreed to be filmed playing with her toddler son for an internet advertisement as a favour for a friend.
When it was aired, viewers were given a glimpse of the new mum. But to her horror, several days later, social services began an investigation into her – even though they knew she was totally innocent.
"I felt violated, humiliated and dirty," Melissa told the Mail On Sunday.
"The whole thing was terrifying. And it made me really angry.
"I had done nothing but had somehow been accused of a crime. I just couldn't believe anyone could even contemplate that I would do such vile things.
"I cannot describe how devastating it was to watch the social worker lift my son's arms, I'm assuming to examine them for bruising.
"To have my fridge checked because someone had accused me of starving him. It was the most humiliating and shocking experience.
"And at one stage I really thought my son could be taken from me."
What Melissa, 40, didn't know was that social services were sure there was no truth in it. However, they had no choice but to investigate the allegations.
And all because Melissa had been increasingly targeted on Twitter. Trolls were intent on ruining Melissa's life by fabricating wild accusations against her. Some called her a kidnapper because she had fought a court battle with her son's father over maintenance and custody. Others labelled her a prostitute and threatened her life.
The broadcaster said some even directed themselves at the companies she works for as a freelance TV presenter, in an attempt to sabotage her career.
Now Melissa is speaking out about the abuse people such as herself and historian Mary Beard are suffering from cyber-bullies.
"I completely understand that social services must investigate complaints, but these vile trolls must be stopped," she said.
"Because of them I had to endure having my son's bedroom looked around and having my interaction with him monitored to see what our relationship was like.
"It was very intrusive and quite terrifying. The social worker told me it was all standard procedure but, even so, I cried when she left.
"The social worker also phoned my doctor, who was asked what sort of mother I was."
Three weeks after the investigation, social services filed a 14-page report that described Melissa as a wonderful, caring mother and said the case was closed.
"It was a huge relief but I felt so angry that these bullies with their lies could put me, and indirectly my son, through so much," she said.
Melissa's ordeal began in August last year after she had just won a High Court battle against her ex-partner, an American financier, over their young son. He had accused her of abducting the toddler – who was born in America – when she remained with the boy in England after the couple split in 2011.
The presiding judge, who called his defence highly misleading, awarded custody to Melissa. The episode cost her more than £200,000.
"I'd never had any interactions with the police and I'd never sat in court before. It was terrifying, the worst experience I've ever been through," said Melissa.
"But when I won, I thought that would be it."
But that was just the beginning of her ordeal.
"When I read the first tweet that I was a kidnapper, I just fell to the floor and sobbed," she said.
"I contacted Twitter straight away but they just said that they were a public platform which encouraged freedom of speech and that there was nothing they could do.
"Then the police visited my home and revealed they get thousands of complaints like mine.
"I went to court and got a non-molestation order out against the ringleaders. "But it's not worth the paper it's written on, as they continue to abuse me. One male judge I saw was very dismissive about the whole thing. He was an older chap and didn't understand what tweeting was.
"While I have the utmost respect for our legal system, I have lost a degree of faith in it. My appeals fell on deaf ears.' She said the attacks have had a devastating effect on her life.
"Bullying hurts no matter how strong, thick-skinned, brave or articulate you are," she said.
"I know I'm not a kidnapper or a prostitute and don't think I deserve to be dead. But some days I just don't have the energy to deal with this."
She added: "My primary concern is my son's happiness. I'm very, very worried about him being able to access all my internet history when he's older and being able to see mummy called a kidnapper."