Wait a minute - I'm not sure that you can make an accurate diagnosis of narcissism (OR ADHD) in the presence of thyroid cancer and a brain tumor.
Both of those things can seriously impair his thinking and memory so it's no wonder he can't get her to her karate classes.
Serious personality changes can happen with a brain tumor (benign or cancerous) and, to a lesser degree, with thyroid hormone imbalances.
So - even if he's always been a jerk, your approach to dealing with him right now has to take his serious mental handicaps into account.
Maybe it would help to look at him like someone with Alzheimer's. Would you expect your grandmother with Alzheimer's to get her to karate on time? Or would you make other arrangements to get her there, or perhaps take her out of grandma's care altogether?
If your ex is having so much difficulty, would he be willing to give up some custody? (Let him be weekend Disneyland dad and you have her during the week?) Or if not, can you document everything and then go to court to reduce his custody (as it sounds like his judgment and memory are impaired by his medical problems)?
Also - for your daughter - two things. First, look up data on phosphatidyl serine and ADD. It's a benign supplement that was shown in one study to work as well as Ritalin for kids with ADD, it's not a stimulant and usually no side effects.
Second - does she really have ODD, or could she possibly have some OCD instead? An older, but excellent book on the subject is The Boy Who Couldn't Stop Washing by Rappaport. Also an excellent parenting book for kids with extreme personality traits is Raising Your Spirited Child by Kurcinkas.
