I would write her a letter explaining professionally that what she has done has betrayed your trust. Explain that whilst working for someone, you may come across information of a private and personal nature and that it is a betrayal of trust and extremely unprofessional to speak to anyone about it and that it would be a sackable offence.
Explain to her that you are devastated that you were unable to share the happy news because it had been already spread. and that whilst you valued the time she spent looking after your children, that you are dissapointed by her behaviour.
It really does need pointing out to her in black and white.
What happens after she receives the letter is down to her, but a grovelling apology should be forthcoming. You will also equip her with the knowledge to know where she went wrong.