Jayne Hickey and her son Christian were shot when two men knocked on their front door in Gillingham Road in Eccles, Salford on 12 October.
The gun was one of two firearms seized when a vehicle was stopped in Faulkner's Lane, Mobberley in Cheshire on 15 December at about 21:20 GMT.
Two men have appeared in court charged with possession of firearms.
A weapon has also been linked to a man's shooting in Ashton-in Makerfield, Wigan on 30 March.
A gun that is believed to have been used to shoot a mother and her seven-year-old son has been seized by police.