So questions: 1) All salary needs to be reported and payroll taxes need to be withheld, correct?; and 2) Is our nanny's compensation par with the market in NW DC?
Yes to both questions. Its bad faith to try to keep renegotiating your contract in such as short time. Its also a very bad sign for the nanny to be asking you to do illegal tax practices especially when she knows that you need to pay her legally. If you and your partner do decide to increase the salary, I would honestly search for a new nanny not reward this type of behavior. No matter what you do she will be trying to manipulate you.