'RHONY's Leah McSweeney Scores Legal Win in Lawsuit Against Andy Cohen, Bravo

"Real Housewives of New York" star Leah McSweeney won a major legal battle this week ... because a judge has shot down a request by Andy Cohen and Bravo to move her lawsuit against them into private arbitration.

According to court documents, obtained by TMZ, Andy and company litigated some of the case in federal district court ... only to then ask for it to be moved over to private arbitration after some initial rulings. The judge said it was too late for that move, ruling the defendants had already waived that right and can't "have their cake and eat it too."

As a result, it looks like the court proceedings will continue to be held in public through the court system. Page Six was first to report the news.

As we reported ... Leah -- who also starred on the 'Housewives' spinoff "Ultimate Girls Trip" -- accused the defendants of creating a toxic work environment where her mental health and alcohol use disorder were exploited all in the "name of selling drama."

In court papers, Leah said Andy and others were pressuring her to consume alcohol during her time on the show -- despite knowing of her addiction struggles.

A rep for Andy Cohen previously told TMZ … "The claims against Andy are completely false."