Two crews and a hovercraft from Weston-super-Mare were called just after midnight to rescue two adults and the children from Uphill beach.
The police and ambulance service also attended, the fire service said.
Avon Fire and Rescue have warned people not to park or walk on the beach in the dark due to the fast-rising tides.

The prince was welcomed to the village of Surama in the Iwokrama rainforest with a feathered headdress, before he watched a cultural dance around a pole.
He met rangers to learn about the steps being taken to protect the rainforest and the benefits of eco-tourism.
Prince Harry later visited a school and the Kaieteur Falls - one of the world's largest freefall waterfalls.
On the penultimate day of his Caribbean tour, the prince took a flight to the Iwokrama International Centre which has a close link to the Prince of Wales, who has been its patron since 2000.
He then visited Fairview village to pay his respects to its elders, as well as going to the local school.
The prince was also taken to an open-air community hall, where he was given presents including a painting of traditional homes.
He gave a speech which praised the people of the remote community, saying: "My father told me what an amazing time he had here, when he was far younger and had far more hair.
"The positive thing you are doing here, it's incredible, your leadership is so important to ensure the protection of this place."
The final stop of the day was the Kaieteur Falls, which has a drop of 250 metres - five times as high as Niagara Falls.
Earlier in the week, the prince met Barbados's biggest star, Rihanna, when the pair sat side by side at a celebratory concert. They also both took part in a HIV test to highlight World Aids Day in Bridgetown.
Guyana is the only English-speaking country in South America.
Between 1780 and 1813, Guyana changed hands between the Dutch, French and British.
Guyana was home to the 1978 Jonestown massacre - a mass suicide by more than 900 members of the People's Temple religious sect led by Jim Jones.
Click here to read more about the country of Guyana

He had rejected a move to Birmingham on Wednesday but has now agreed personal terms and passed his medical.
Stewart, who was in the final year of his contract at at Dens Park, had scored six goals in three games for Dundee already this season.
He could make his Blues debut in Saturday's Championship match at Leeds.
Stewart is Birmingham's second signing of the week following the arrival of striker Che Adams from Sheffield United.
Birmingham opened their Championship campaign with a goalless draw against Cardiff City and were knocked out of the EFL Cup by League One side Oxford United in Tuesday's first-round tie.

3 October 2016 Last updated at 13:34 BST
Greater Ardoyne Residents Collective (GARC) supporters, including spokesperson Dee Fennell, confronted the high-profile priest after the Orange Order Parade passed the Ardoyne shops.
A small crowd of protesters accused him of taking sides with Sinn FÃ©in and the Orange Order against a majority of local residents.
Fr Donegan has ministered in the Ardoyne area for the last 15 years, and is due to take up new duties next week at the Tobar Mhuire retreat centre in Crossgar.
A family of five, including three young children, had to be rescued from a Somerset beach after their car got stuck in the mud on Saturday evening.
[NEXT_CONCEPT]
Prince Harry has visited the heartland of Guyana and explored its rainforest on day 14 of his Caribbean tour.
[NEXT_CONCEPT]
Birmingham City have signed Dundee forward Greg Stewart on a three-year deal for a fee believed to be around £500,000.
[NEXT_CONCEPT]
Fr Gary Donegan was confronted by a small crowd of angry protesters following Saturday's Orange Order march in north Belfast.