I assume you're talking about the powder blue coat she wears in several scenes. Right?
Be attentive to that coat. It has paint stains on it and the colors are of the sets in her kids' vaudeville acts. This is a Mama Rose who not only devises the routines, she paints the sets as well. It symbolizes all the things she's done for her kids.
LuPone removes the coat at the beginning of "Rose's Turn" when she stops living for her two daughters and realizes she should be living for herself. She either kicks it into the wings or tosses it there (depending on her mood at that performance) in a gesture that symbolizes her tossing away her past.
Didn't you ever learn to watch a performance carefully?
"Long live God!" (GODSPELL)