"I wanna say thank you to @shannonbeador @oclydia @rhoc_kellyddodd (youknow what you did and you all rock)," she said of co-stars Shannon Beador, Lydia McLaughlin and Kelly Dodd. "#arubaido."
Judge originally married Eddie in Dana Point, Calif., in June 2013.
She shares son Ryan with first husband Darren Vieth, and is parent to Sidney, Sophia and Spencer with second husband Simon Barney, who took custody of Sidney after their divorce.
E! News reported Sidney called out Judge in a since-deleted post Monday, saying she ultimately chose to live with her father because of her mom's "toxic" behavior, not because of the divorce.
"The reasons I left my mother's house are that she was neglectful (leaving us at home with no food or simply ignoring us entirely), she constantly put herself first and the biggest reason was that she was mentally and emotionally abusive," Sidney wrote. "She was no mother to me."
"The ONLY reason I am not living with her is because she continues to do the things that pushed me out of her house, like talking about me on the show/press/social media, doing embarrassing things on the show, lying to me and putting herself first to name a few," she added.
Judge described the situation with Sidney as "so messed up" in an interview with "Entertainment Tonight" in August 2016.
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