
Here she is in 1979. Judge for yourself.
Not sure when she first fell off the wagon, but it was presumably sometime after she married Fat Boy.
The answer may be found in the following article from Boston Magazine:
That famous accident, which would dash any chance Ted Kennedy had to become president, occurred on a sultry July night in 1969, when the senator drove off a bridge on the island of Chappaquiddick, at the eastern end of Martha's Vineyard. A young woman named Mary Jo Kopechne was beside him. His car plunged into a shallow waterway, Poucha Pond, landing upside down. Kopechne drowned; Kennedy swam to shore, leaving her body in the water to be found by Edgartown police. Afterward, his wife stood by her man, even at Kopechne's funeral. Already pregnant with another child, Joan would lose the baby a month later. "For a few months everyone had to put on this show, and then I just didn't care anymore. I just saw no future. That's when I truly became an alcoholic," she told Laurence Leamer.