The post on Instagram showed the family enjoying rides at the California attraction, drawing comparisons with Prince Harry's childhood trip to Florida's Walt Disney World with Diana, Princess of Wales, in 1993.
The montage also features a clip of Archie, six, and Lili meeting Disney princess Elsa, from the film Frozen.
Meghan wears a Minnie Mouse hat in some of the snaps featured in the video, while another image shows a two-tier Little Mermaid-themed birthday cake for Lili.
The duchess captioned the video: "Thank you @disneyland for giving our family two days of pure joy!"
The footage was reminiscent of photos taken of the duke when he was eight and his mother Diana took him and William to Walt Disney World.
At the time, the royal siblings were photographed sitting at the front of a log on the Splash Mountain ride, with adults from their mother's entourage behind them and Diana seated at the back.
Meghan's post follows several family shots in recent days to mark Lili's birthday.
In one, she posted a throwback video of herself twerking in a bid to bring on labour while pregnant with the princess, while another post featured a black and white snap of her cuddling Lili.
In another post, she described how Lili's relationship with Harry was "the sweetest bond to watch unfold".
She shared two photos of the princess with her father, the duke, adding: "Daddy's little girl and favorite adventurer. Happy birthday Lili!"
Lili - the Duke and Duchess of Sussex's youngest child - was born on June 4 2021 and was named Lilibet Diana Mountbatten-Windsor.
Lilibet is named after her great-grandmother, Queen Elizabeth II.
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