If you have a narcissist for a parent, you live in a world governed by whim enforced without mercy.
Narcissists have normal, even superior, intellectual development while remaining emotionally and morally immature. Dealing with them can give you the sense of trying to have a reasonable discussion with a very clever six-year-old -- this is an age when normal children are grandiose and exhibitionistic, when they are very resistant to taking the blame for their own misbehavior, when they understand what the rules are (e.g., that lying, cheating, and stealing are prohibited) but are still trying to wriggle out of accepting those rules for themselves. This is the year, by the way, when children were traditionally thought to reach the age of reason and when first communions (and first confessions) were made.
Having a narcissist for a mother is a lot like living under the supervision of a six-year-old. Narcissists are always pretending, and with a narcissistic mother it's a lot like, "Let's play house. I'll pretend to be the mother and you pretend to be the baby," though, as the baby, you'll be expected to act like a doll (keep smiling, no matter what) and you'll be treated like a doll as an inanimate object, as a toy to be manipulated, dressed and undressed, walked around and have words put in your mouth; something that can be broken but not hurt, something that will be dropped and forgotten when when something more interesting comes along. With narcissists, there's also usually a fair element of "playing doctor," as well of childish sexual curiosity that may find expression in "seductive" behavior towards the child, such as inappropriate touching of the genitals, or it can also come out as "hypochondriacal" worries about the child's health and/or being most interested and attentive when the child is ill (thus teaching the child that the way to get Mother's kind attention is to get sick). Having a sick child can also be a way for the narcissistic mother to get the sympathetic attention of authority figures, such as doctors and teachers.
Problem is too that toddlers or 6 year olds grow up; narcs remain at such an emotional age.
Re this part of your comment 6monthsin:-
"I am thinking about counselling. I keep wondering whether in fact I'm the narcissist and am making this all about me, and should be kinder or more patient or more receptive towards her. It's so confusing"
Counselling may well be very helpful to you but counsellors are like shoes; you need to find someone who fits in with you.
And no you are not a narc either, narcs would never ever ask themselves such questions to begin with. Being kinder to a narcissist only gives you more aggravation in the long run.
With regards to your child I would keep your child at arms length from her anyway. This is because narcs do not make for being good grandparents and in your case as well your mother certainly has what they need i.e a willing enabler - your Dad - to help her.