Kate Hudson has been documenting sweet moments with her kids Rani, Bingham "Bing," and Ryder, from their family vacation

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Kate Hudson, Rani
Credit: Kate Hudson/Instagram; Inset: Rodin Eckenroth/FilmMagic

It's all fun in the sun for Rani Rose!

On Monday, Kate Hudson, 42, shared an adorable series of photos of her 2½-year-old as she played in the sea during their family vacation to Greece.

In the snaps, posted to Instagram, Rani, whom Hudson shares with boyfriend Danny Fujikawa, wades in the water while wearing a too-cute yellow romper. Rani flashes a big smile as she runs through the sea and turns back for the camera.

The mom of three simply captioned the photo with a shining sun emoji.

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Kate Hudson, Rani
Credit: Kate Hudson/Instagram
Kate Hudson, Rani
Credit: Kate Hudson/Instagram
Kate Hudson, Rani
Credit: Kate Hudson/Instagram

Throughout their family trip, Hudson has documented several sweet moments with her kids Rani, Bingham "Bing," 9, and Ryder, 17, on social media.

Last week, Hudson shared a picture to Instagram of her cuddling her two youngest children, writing that the family was still "waiting on big bro."

"We miss you @mr.ryderrobinson#hurryupandgethere," she added.

When Ryder arrived, the Bride Wars star snapped a selfie with her eldest child, writing on Instagram, "Look who just got here ❤️🧿❤️ #familycomplete"

Speaking with PEOPLE last month, Hudson opened up about how Rani is quickly becoming her mini-me.

"She wants to work out with me," said Hudson. "She gets on there, she's doing her butt exercises. She kind of does her own version of them. Turns into a little bit more of a dance move. I'm learning so quickly that this whole 'everything that is mom's is yours' when you're a girl is real."

Hudson added that she plans to pass down some of her favorite fashion pieces to her daughter, explaining that she never got to raid Hawn's closet for her stylish red carpet looks since "Mom is really good at purging and not keeping anything."

"So she kept none of her old clothes, and when I got older, I was like, 'Where are those Alaïa pumps, Mom? Where did you put all of those amazing dresses you wore?' And Mom's like, 'I don't know,' " said Hudson, adding of herself doing the "opposite": "I have everything. I was looking through some of the archives, and I said, when Rani is 16 and opens up this box, I'm going to live through her."