Rod Stewart's Ex-Wife Alana Says She's 'So Happy' for Son Sean After His Impromptu Vegas Wedding

Alana Stewart is supportive of her son Sean Stewart's "spur of the moment" marriage to Jody Weintraub, which PEOPLE exclusively revealed via a source close to the couple on Monday.

"Congratulations to my boy @seanstewart and his beautiful bride @jody_weintraubstewart who surprised us all with a spur of the moment Las Vegas wedding," the proud mom wrote on Instagram early Tuesday morning, confirming Sean's news.

"I'm so happy for you both!👰‍♀️🤵🏻❤️🍾🎂," she added.

The entrepreneur, 42, proposed to Weintraub, also 42, on Valentine's Day during a trip to Las Vegas last week, and the duo headed straight to the courthouse the same night.

"Sean asked her while they were out to dinner at Catch. They married shortly after getting their marriage license at 10 p.m. at Little Church of the West," a source close to the couple exclusively told PEOPLE.

The Dirty Weekend streetwear designer has known the former Extra producer, daughter of the legendary late producer Jerry Weintraub, since high school, the source explained. "They are both very family-oriented people."

Sean's dad is rocker Rod Stewart, whom Alana married in 1979. The couple divorced in 1984, but they've remained friends. Alana also shares daughter Kimberly, age 43, with the British "Maggie May" singer, and has a son, Ashley Hamilton, 48, with film star George Hamilton, 83.

As for Sean and Jody's last-minute nuptials, the couple intended on just taking a typical romantic trip for Valentine's Day to the Wynn hotel, but then it quickly turned into a lifetime commitment. "Sean and Jody share a best friend, Courtenay Semal, which was the reason why they kept reconnecting over the years. They both have famous families, they just get each other," the source shared, noting that the couple is "so much alike" and are "born two days apart" from one another.

After Sean's sweet proposal, he called his mom on the way to the courthouse, and the source said that it took her a minute to really know if he was serious or not, "as he's known as a bit of a jokester in the family."

When they sent her photos and videos after making it official, "she cried" and was "so so happy for him." Sean also talked to his dad, Rod, who was performing at the Hard Rock Hotel & Casino in both Tampa and Hollywood, Florida. "His dad was so happy to hear the news," the source said.

When Rod, Sean and the new Mrs. Stewart arrived back to L.A., the source added that they celebrated at Nobu in Malibu, as mom Alana posted to her Instagram Story on Tuesday, showing a shot of herself in the clip with a beaming smile.

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Sean, who is "really close with his mom," is now a loving stepfather to Jody's 5-year-old son Doc. He has been house-hunting with his new wife and is "proud" to finally have a family of his own. He and Jody also want to have children together. According to the source, the newlyweds plan on having a traditional wedding this summer in Spain at Marbella Beach Club with their families.

"They're the same person," the source said of the couple and why it works. "They're from the same town, they have the same friends. They just understand each other."