As I said pages ago...those who feel kids shouldn't be excluded will likely never be convinced otherwise...those who feel that the invitees should honor the wishes of the bride/groom will likely not change their minds either.
OP - one thing though. IF you decide not to attend and even with your decision not to be in the bridal party - this is YOUR CHOICE. You are likely going to permanently affect your relationship with your sister by this choice, and it sounds like you are willing to do so over her disagreement with you on whether children should be at a wedding reception. Fine, if that is a big enough belief of yours, I GUESS it's worth losing a member of your family for. But make sure to bank away in your mind, for 20 years down the road when you start thinking how and why your relationship with your sister isn't a better one, that is was YOUR CHOICE to do this. You might accidentally start thinking it was hers....but no, she just wants an adults-only reception, which thousands of people agree with - she's not completely out of line with that. So you are making the choice that will affect this relationship forever. Just make sure it's the decision you want forever.
And 'choosing' your daughter over your sis?? Over a 9 year old not being invited to an adult reception? My goodness, if my kids ever felt that I was choosing someone else over them for attending an adult event - well, let's just say that it's likely a good thing that they realize that the world doesn't revolve around them -especially for someone else's wedding! My kids know I would never choose anyone else over them....but attending an adult reception does not fall inot that category IMO and in theirs either.
My sisters and I are VERY, VERY close and my kids are basically like both of their own too...One sister who got married after the other 2 of us had kids - had an adult reception. Honestly it never would have occurred to me to be upset at all about it. I got the reception I wanted, why on Earth would I want her to have anything but the reception that she wanted? And the other sister DID have kids at hers....because she has some relatives on dh's side who would have thrown a fit if kids weren't invited and likely would have caused a rift due to them not attending because of this. They are known for being angry when kids aren't invited. SO, my sister caved and had kids at her wedding - NOT because it was what she wanted, but because some very selfish people in her husband's family dictated what they wanted instead.