Jamie Woodrow, 33, appeared in Hull Magistrates' Court on Saturday, charged with robbery, possession of an imitation firearm and possession of an offensive weapon. He entered no plea and was remanded in custody.
A 25-year-old man is due to appear in the magistrates' court today for charges of robbery and possessing a knife in a public place.
Detective Sergeant Matthew Peach said: "I would like to reassure residents that this is a rare and isolated incident.
"We are working and supporting the family who were clearly traumatised by the incident, I would like to stress the children were not harmed.
"I urge anyone who has any information or witnessed any suspicious activity in and around the Arthur Street area of Withernsea on Thursday evening to please come forward by calling 101."
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