Lady -

Sleep problems with MS are so common and so many MSers go though it. I generally do not fully wake up during the night. (Although, I do take Neurotin before bedtime and that keeps me "asleep" for the night). I partially wake up with spasms and quite often sleep restlessly (jerking around in my sleep) - but still do not wake up fully during the night.
I don't have any suggestions other than using a dim light and/or night light in the bathroom. Brighter light sends signals to the brain to wake up and for many people (MS or not) once the light goes on, they have a hard time getting back to sleep. It's worth a try.
I would also talk to your dr about this as they may want to do a sleep study on you and/or make other recommendations. Not getting the quality sleep does have an effect on our cognition. Think of those studies they did on over tired drivers vs. drunk drivers. Over tired drivers consistently did worse than drunk drivers.
Try some of the suggestions others have made and let us know how you are doing.