The vehicle drove into the home in Hale Village, Liverpool at 9am on Sunday, running down a fence and into the family's car parked outside before smashing into the hallway.
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It took out a portion of their wall and a structural beam, the Liverpool Echo reports.
But despite the accident leaving a giant hole in the house, the family say insurers LV told them they couldn't send anyone out to help until Monday, leaving them to deal with the problem overnight.
Chris Wallis, whose uncle owns the property, said he was told about the accident - which happened while the family, including two young children and his 70-year-old grandmother were in the house - this morning.
He said: "We've been on the phone to LV insurance since 9am this morning - they say it's not an emergency.
"We've spoken to about 15 different people but there is nothing they can do, they are saying.
"They kept telling us it's not a home emergency, it's a building problem and they don't work weekends."
Chris added the family called LV at 9am before waiting for hours for a response.
Four hours later, they tried to call the company again before a man was sent round - with the brief that he was simply patching up a hole.
According to Chris, when he saw the true extent of the damage, he said he couldn't touch it because it was too serious - and now the family face a night with a large part of the front wall of their house missing.
As a temporary measure they have used old fencing to attempt to block the gap for the evening.
The car struck in the hallway metres away from where Chris's grandmother would have been sleeping in her downstairs room, forcing the family to use the back door.
Chris added: "There are two young kids in there and a 70-year-old woman who have to spend the night like this."
He said LV have offered the family alternative accommodation, but they were reluctant to leave the house unprotected.
LV and Cheshire Police have been contacted for comment.