well i think she did the right thing opening it as the letter wasnt addressed to anybody-it just said urgent and this could have been anything -the mother shouldnt throw it away and ignore it, her daughter could need support.
the mother shouldnt tell her daughter off, but explain gently she was concerned about this strange urgent letter, thought something bad had happened so read it, and explain what she read. The daughter may be embarassed, however may really appreciate somebody to talk to about it, and a quick talk from her mum to say going off with a married man is a bad idea wuldnt go amiss-it only ends in misery.
Chances are the affair ended long ago if the wife has had a baby, and the daughter has moved on, but she still may need some support anyway-whos to say the married man wasnt leading this daughter on as they often do?
it will be a weight off her mothers chest-and a lesson/chance for support for the daughter.