I have Type II diabetes. By going low carb (now primal) I have been able to drop several drugs AND achieve normal blood glucose. My mother is very proud of me and told my brother, his three daughters and fiancee.
After my father's funeral, we took over a 16th century country pub for lunch. The chef agreed a menu with my mother and said he could do whatever I wanted from the ingredients he had.
Even though my mother told them all this, on the day, several of them moaned at my mother because I had 'better' food - and they weren't even contributing to the cost.
So my advice would be to stick to your guns, because if you give in once and eat the food you'll always be expected to eat it.
Your sister may feel that you're eating too 'posh' and she may feel resentful. She may also feel guilty about giving her kids processed foods. She might not want you bringing stuff because she thinks it threatens her hostess with the mostess reputation.
Personally I'd spread the word that this is not some yo yo diet fad to other relies and would bring enough food to spare for other people as well. I'd tell the kids they could eat what they wanted but if they felt unwell afterwards if t was on them and I'd let that be known too.
If she kicked off on the day, I'd tell her that she has no right to dictate how you bring up your kids, get OH to back you up on it. Point out you ate some of her food but also brough enough of yours to share, that you're allowing kids to eat it as a treat and that if she is going to continue having tantrums about what you and your family eat you just won't come to her house anymore.
I'd offer to host next year and show Primal isn't as weird as she thinks.