Sorry for the echo, but, yes, some disagreement is normal, but lots of harmony and fun is also normal. I've noticed that my two daughters, 8 and 5, fight when they are trying to jockey for power, like who gets to chose the game, or, the old: "who's right" game (this one can take many forms). I remind them about twice a month that they are not each other's mom, but each other's best friend. This tends to turn things around and they can look at each other in this new light. I grew up with a brother one year older and a brother one year younger, and I always used to pine for a sister. I thought that a sister would just make my life 100% better. I loved my brothers (and still do), but they had the ability to be very, well, active, when a good tea party or make up party would have suited me better. It was especially bad when they had a group of boys over to play. Thank goodness I had my own room.
Anyway, I was so glad that my girls got a sister and I think I have that vision of "best friend sisters" that I totally promote and that they, for the most part, buy. I don't get involved in their squabbles very much except to insist that they resolve conflicts respectfully (but that true of their conflicts with everyone). It is a great joy to me then to leave them alone and soon hear their giggles. They even made up a chant where one says :"sisters" and the other says "sisters"; then one "fovever" the other "forever"...and this goes on and on. It's music to my ears. I have told them that any toy or issue or whatever is temporary but their sisterhood is forever.
Maybe Grandpa's comments were helpful because subconciously he is showing them a vision that there is another way for siblings to be.
All the best in dealing with this,
Cathrin