The problem is the cat's out of the bag.
Open source image generators already exist and have been widely disseminated worldwide.
So all you'd end up doing is putting up a roadblock for legitimate uses. Anybody using it to cause harm will not be seriously impeded. They can just pick up the software from a Russian/Chinese/EU host or less official distribution methods.
It would be as effective as the US trying to outlaw the exporting of strong encryption standards in the 90s. That is to say, completely ineffective and actually harmful. Enemies of the US were still using strong encryption anyway.
Standard Ubuntu should have you covered.
One word of warning though, don't be too egregious with the parental controls. If your kids are motivated enough, they will find a way around it.
Education really is your best weapon here. Tell them about the dangers of the modern web and computing.