More than 7,000 people shared shocking video footage on social media showing the children in the boot with just 'two iPads, blankets and a glass of water'.
Another video shows the alleged father being walked to a police van after being arrested, members of the public shouting at him and one commenting 'clearly not a dad then'.
The video footage of the incident which allegedly took place on Saturday night at Planet Fun in Sea Lane was recorded by Sam Mellor and posted on Facebook.
He said: "Two kids were left in a car with doors locked and windows up.
"One boy and one girl - very young - were left in the boot with two iPads, blankets and a glass of water
"Security told everyone to leave and not to smash the window or they will be arrested for criminal damage.
"Even when the boy put a bag over his sister's head suffocating her, the security still told everyone not to smash the window.
"The window got smashed and then the father come back from his night out saying he was coming back to check on his babies.
"He was detained. He was very lucky the police were there as a load of people were waiting for him to get hold of him.
"Disgusting security and disgusting father."
More than 1000 people commented on the post. One comment said: "Security should be disgusted with themselves!
"Children come first not the car! Dad should never be allowed to see them again if that’s how little he thinks of his own children!!
"He is scum. There’s people in this world that can’t have kids and you’ve got a father like that!"
Lincolnshire Police have confirmed a man in his 40s has been arrested. In a statement they said: " We received reports of two children who had been left unattended in a vehicle at 10:29pm on Saturday August 28 at Planet Fun on Sea Lane, Ingoldmells.
"A man in his 40s was arrested on suspicion of child neglect and was released on bail pending further investigation."
Anyone with information should call 101, quoting incident 499 of August 28th.