Don't know the history of Molly,but will try find out for you as I'm rather interested in it myself.

I do know that the term "tart with the cart" does not refer to Molly per se ! but however is a reflection on Dublin wit. Many the monument gets jibes in such satire-like prose. The Anna Livia fountain in O'Connell Street was known as "the flussi in the jacussi" or the now removed millenium clock from the liffey as "the time in the slime".Such is the humour !

Diesel - in Dublin