Hiyas. I feel like you are getting hammered because your kid ate the normal way people feed their kids until you discovered primal. I don't think that's very fair, really, because you probably didn't know any better. Heck, many of my own family members let their kids "sip" their diet cokes and coke zeros and whatever else -- since they drink so much of it, so do their kids. I'm the weirdo who doesn't let my kid have soda.
Luckily, though, I live in a community where it's fairly common for parents to have their kids on various "clean" diets. Some are gluten free, some are vegetarian, but nearly everyone is whole foods. And we are the "bad parents" who allow our kid sugar about once a week (usually 25g of candy or chocolate). And, we also make natural soda (fermented beverage) o r buy locally made fermented sodas. Or, we do fresh juice with seltzer water.
Families give us the old-tisk-tisk, but you know, we probably tisk-tisk over the number of processed crackers that their kid eats. LOL Or grains. Most of them eat a lot of grains.
Also there might be some people here who tisk-tisk at me because DS is allowed to have rice, gluten free buns, and whatever breads his friend's mother makes. It's usually less than 3x a week, and it's not like he's eating a loaf of bread each time, you know? It's just easier to let him have it than to worry about it.
Thus, my recommendation is as follows.
1. discuss with your partner what a good balance for your family is in terms of "treats" and grains and the like.
2. once you know what this is, you can put some rules around it such as "sodas are a treat for sunday" and you can do things like A. make your own (it's a fun project -- go on youtube and look for videos. it will shock you with the amount of sugar used, but the fermenting bacteria feed off of that; you can also make water/juice kefirs which are sweeter than those horrid kombachas), or B. buy naturally fermented soda, or move to the seltzer/juice mix (1/4 juice, 3/4 seltzer).
3. limit grains and sweets as you see fit. In our home, there are no grains (we do quinoa or millet, and since the millet is local, we usually go for millet which is a seed), but we do have dark chocolate and we are transitioning to making our own (raw cacao, coconut oil, local manuka honey, and whatever else we want to put into it). We do sweets like GF cakes or even candies or good organic gelato on an intermittent basis such as once every month or two. This works for our family.
Beyond this, you need to get and agree upon a clear picture of your daughter's health and well being. she might be a larger girl -- and there's nothing wrong with that. It may be that she looses this weight later, as a previous poster mentioned that she grew to a certain size by a certain age, and that was that. And, you may decide that she is overweight, and as such, you need to make familial changes.
I would recommend, btw, a family walk after dinner. It's something that we do and enjoy a great deal. We also do a long hike before our breakfast (DS has breakfast, we hike, and it's his lunch -- it's technically more brunch like) on Sunday. We do 20 minutes at the park before driving DS to school.
We do this because DS needs to burn off energy -- this helps keep him grounded. He needs to be outside, you know? And guess what? So do we. By doign these things as a family, we are improving everyone's health. It's small things, done over time, consistently that lead to good positive results.
Good luck with it all!