also regarding severance; any severance you provide can count against her unemployment benefit; i don't know if it reduces your tax liability later but i think the max is 5% of the first 8000 you pays about $400. I think you can't claim unemployment against someone unless you work there at least 3 months but i could be wrong on this

You are not obligated to give severance; it is nice to do so and will make the final blow (firing) easier; but it does not guarantee peace of mind. she doesn't sound like someone who would appreciate that you are paying her when you don't have to , she likely feels entitled.
It helps to have documented evidence if she is grossly negligent or simply failing to meet standards that you have set out and that you have discussed with her, this is for the purpose of the call you will get from unemployment or if of any reason she tries to sue you. You can try and sit down with her but so far doesn't sound like she is the type of person to improve. Like any employee, sitting down and going over expectations and performance is helpful; but if it is pulling teeth to do this with her, just save yourself the headache and move on.
the longer you keep her the more likely you can be entangled in drama or legal issues. Just because they had a good reference from other people does not mean they will be a good fit for your family -- different families have way different expectations.
I found the hard way that hiring from this website, many people touting their nannies are actually getting rid of them. Don't feel like you are a bad person for not being able to work it out with her -- get someone thats maybe not perfect but you can feel really good about. There are plenty of people that will jump through hoops for her job.
good luck to you.

Keep in mind that if she is unable to find a new job and applies for unemployment benefits you may be facing increased unemployment taxes. This could be anywhere from a few hundred $$ to $1000 per year. The exception is if you fire her for cause - and are also able to prove to the relevant unemployment agency that you terminated her for cause, which is actually very difficult to do. Most states, including MD and DC are incredibly pro-employee on this issue. It also may put you in the uncomfortable position of having to go through a semi-adversarial process of having to explain why you terminated her to the unemployment agency. If you are terminating her for cause, I would provide written notice stating that you are terminating her for cause. If you think this may become an issue, I would spend a little time googling this and/or reading other posts on DCUM about this.

You should have a sit down with her and discuss these things with her. Give her a time period to make these changes. And document everything. During this period, interview other nannies and if she changes, great. If not, fire her, without severance, and you will have a new nanny already lined up.

Considering she hasn't done anything grossly inappropriate, it would be heartless to tell her that today is your last day and that's the end of your income. It doesn't sound like you have given her a warning, so this will come out of the blue. Unless you're giving notice, it will be kinder (and honestly, think of karma) to give her severance. If two weeks sounds like too much, give her one week. Just put yourself in her position - she has no idea you're not pleased with her work, she's getting fired from one day to the next, has no job lined up, and loses her entire income.