If it was me personally, I would stop letting her mind my dd - Lucozade is VERY dangerous for young children (it's not great for adults, either, unless they are sports training), and it seems like your mother has no respect for your wishes or your rights as the mother of that little girl. Makes me wonder what else she is doing that you are not finding out about - if you were looking for childminders, would you pick one that didn't listen to what you said and didn't have much common sense?
That's just me though. If you don't want to do that, perhaps you could get her to look on the bottle, or the website, which clearly states it is not suitable for children?