apparently the US authorities do not have any legal access to UK legal databases so there is no way they could get hold of information regarding your arrest. This does not apply if you have committed such crimes as drugs or terrorist offences in which case the authorities here are obliged to share the information. I suspect there are thousands of people travelling to the US on the visa waiver scheme in your situation who simply tick no to all of the questions on the form. If everyone who wanted to go the US on holiday applied for a visa the embassy would be inundated. I don't think that the Americans are really that interested in petty crimes, they are very much more concerned with drugs and terrorism. The fact that your children don't have the same name as you shouldn't be a problem as they will no doubt have their own passports. My neice has travelled several times with her children, they do not have the same name as she does.