I had this problem, it appears that the Nabi servers are down (maybe permanantly?)
To enter mommy or daddy mode though, turn off the wifi - you can either do this in the settings (within the kids mode) or its easier to just put it into airplane mode (hold down the power button and there should be an option there)
Or go somewhere where there isn't any wifi
Then log in to mommy mode as normal
It would seem that if the tablet is connected to wifi, it checks the password on the internet, and seeing as there is a problem it returns an error.
I imagine though that you might not be able to change the password as currently you can't log into the Nabi account via the Nabi website.