Long reported to be less-than-cordial, the pair's rivalry "is alive and well," says the source, after the recent slight.
Pink, aka Alecia Moore, recently "suggested she and Gwen bring their children together for a Beverly Hills playdate," says the source.
While Pink raises daughter Willow, 2, with race car driver husband Carey Hart, Stefani and rock star husband Gavin Rossdale are parents to sons Kingston, 7, and five-year-old Zuma Stefani is also pregnant with a third boy.
But according to Radar's source, the "Stupid Girls" singer was shocked when Stefani said no way!
"Pink was pretty upset when she got an email a couple of days later from Gwen that basically said, 'not now and not ever' to the idea that they bury the hatchet by having their small children meet each other,' the source says.
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The pair memorably kissed on stage at the iHeartRadio Music Festival in 2012, but it seems like those days are long gone -- for now.
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