Raimoundas Mecinskas was driving a blue Honda, and talking to his partner on a hands-free set, when the collision happened on Retford Road, on April 7, said prosecutor Emma Cornell.
Witnesses gave descriptions of him and the Honda, and officers found it parked, with a damaged front-end, in a car park that was 500 metres away.
The court heard Mecinskas, aged 48, received a 20-month ban after he was convicted of driving with excess alcohol, in October 2020.
He later said the collision wasn't his fault as another driver failed to give way and crashed into him.
"He heard his young child screaming down the phone and thought it was more important to go to him than stay around and deal with the accident," said Ms Cornell.
Abbey Edwards, mitigating, said: "He accepts making a huge mistake on this occasion."
She said he 'panicked' and drove the short distance home, but made himself known to a police officer as soon as he saw him.
"He is extremely anxious about imprisonment because he is concerned how his child and partner will cope without him,” Ms Edwards added.
Mecinskas, of Cavendish Road, admitted driving while disqualified and without insurance, and failing to stop, when he appeared at Mansfield Magistrates Court, on Tuesday.
He received 14 weeks, suspended for 12 months, with 100 hours of unpaid work.
His license was endorsed with six points. He must pay a £128 surcharge and £85 costs.