Multiple Personalities Support Group
Dissociative identity disorder is a diagnosis described as the existence in an individual of two or more distinct identities or personalities, each with its own pattern of perceiving and interacting with the environment. At least two of these personalities are considered to routinely take control of the individual's behavior, and there is also some associated memory loss,...
Perhaps you could schedule phone appointments with you therapist instead of actually having to go and visit her in an office? This might be easier to excuse to your parents, you just say it's a friend who needs to talk to you about some stuff and you'll be back in a minute.
You don't mention how long they are staying for if its for a couple of days you may find it easier than you thought, if it's for longer then plan some time at the end of the day for your other parts to express themselves in healthy ways.
Also are they staying with you or at a hotel? Perhaps you could suggest that they go out on day trips and things whilst you have "doctors" appointments about physical things.
If you don't feel comfortable with lying to them then perhaps you could tell them that you take a nap every afternoon just to get some space for yourself and your parts. If your parents haven't figured out that you have DID chances are that your parts have cooperated in the past, I'm sure if you ask them they will cooperate again
xxx