MB here - I think you got great advice from 13:21. In general be brief, kind, direct and don't draw it out. Do you have a contract with her? If so, be sure you're in compliance re severance time. If you have a recommendation letter for her give it to her. An actual severance letter might not be a bad idea either - you want to document the severance you're paying, terms (like not returning to the house, returning house keys, other confidential things, contact w/ the children, etc...) How old are your kids? Obviously that comes into consideration re any contact with them right away, and/or long-term.
Have you thought through lock-changing (if applicable), access to car/phone/credit cards or anything else along those lines?
Quick clean and fair is always better. Especially if she's emotional. And having things written down helps also - if she's shocked by this she likely won't have a clear memory of exactly what you said so think about what message you want her to hear. You could write a letter that says something like "dear Jane, As we discussed, today will be your last day of employment with us. Attached is a check for $XX which serves as your severance. Also attached is a letter of reference from me which you can use in seeking future employment. (THink about whether you are willing to be contacted for additional reference info.) We appreciate everything you have done to care for our children and wish you all the best. "
Keep copies of the letter, cancelled check, etc... should you ever need to document severance or terms of the firing.
Think seriously about whether (if you wanted to have her see the kids at some future date) you want her to come to your house again. You could always meet at a coffee shop or playground - somewhere more neutral. You probably won't want her at your house again.
Good luck.