Stuff likes this drives me crazy. They have a right to fire whoever they hire to watch their son. I read part of the complaint and it starts off with gratuitous shots at Imus.
Absolutely they can terminate her at any time for any reason. It's called "employment at will" and unless she had a contract, that's what it is.
However, Imus is too stooopid to STFU. He may pay tuition to find out just how stooopid he is, especially if his charity turns out to be a scam.