It could be a positive, OP? Nobody's cheated, nobody's let you down, and your two boys are possibly going to have an older sister to love them and make a fuss of them. Nobody is going to love your younger child any less for being a boy. He's a unique human being, not simply his sex.
I do appreciate that this is a shock, but you said yourself that the woman doesn't want money, doesn't want anything from your husband or your family. A twelve year old child wants to get to know her father and her baby brothers. That could be a lovely thing for all sides.
Step parenting can be awful, but it can also be fantastic, and you don't have the usual acrimony of a split, and children whose lives have gone horribly awry, to navigate.
Might it be feasible to seek some counselling, at all? Is there a charity that can do that, or can your health visitor refer you? It is such a huge change, but handled well.... well, all babies benefit from more people in the world to love them. Your sons may have a big sister to enhance and enlarge their worlds. It could be a good thing.
I send 
because I appreciate that it has to be a shock, too!