Ms Minnock said her son believed he had been away on holiday and they had been having "normal, fun times together", including going swimming and visiting parks.
She said she decided to hand herself in after Ethan asked to see family members.
Her 52-year-old mother and Butt, 56, told a judge they had no idea of her and Ethan's whereabouts. However, they were arrested and admitted at Bristol Crown Court that they had lied to protect her.
Watch: The police appeal for Rebecca to hand herself in
Minnock was jailed for 10 days and Butt, who drove Ms Minnock to Cheltenham in order to escape the authorities, was given a 28-day sentence.
Judge Stephen Wildblood said he "could not possibly" avoid imposing a custodial sentence after concluding that they had deliberately withheld vital information.
He condemned their "wicked" plot to generate publicity for Ms Minnock's custody battle.
Butt had told the court: "She said she couldn't stand the thought of losing Ethan. She asked if I would help her get away. I said yes.
"The plan was to keep her away for as long as possible and generate as much publicity as possible. I said the press will be involved when you go missing. Then people will listen."
He added: "We have got what we wanted to achieve. We have got the press, we have got the newspapers. Maybe we can make a stronger case. It's the way we planned it and the way it has worked out."
Ms Minnock told the Daily Mail: "I've heard today that my mum's been taken to court and I know it's not fair to Ethan to keep running with him. He needs to go home, he needs his routine back.
"It's been extremely difficult, I've considered it every day since we've gone. What's made my mind up, Ethan has been asking to see my family, he's been asking to go to his bed back home."
Prior to her handing herself in, Judge Wildblood had said: "This mother must not see herself as being backed into a corner because there is a very simple solution for her - come forward with Ethan.
"The strain on this mother now must be immense and, from what I know at present, it appears that matters have simply snowballed from an impulsive decision."
He added: "There is no doubt at all that Ethan is a boy who is much loved by both of his parents and that they both want what they perceive to be best for him."
Ethan has lived with his mother since his parents separated in February 2013. A custody battle began the next month. A judge ruled on May 27 this year that Ethan should live with Mr Williams and have supervised contact with his mother.
