This is nuts, and extremely and unreasonably controlling.
At 14 she should be being given way more freedom. The aim of good parenting is to grow them up into competent adults who can regulate themselves. If they're all hedged about with rules like this, how will they ever learn to manage themselves?
Your rules are suitable for an 8 year old, max. After that, it's still too early, too harsh and too inflexible.
Yes, they should be allowed to make themselves food and drink pretty much whenever (but not necessarily WHATever) they like. You have a conversation with them about reasonable things, so not eating food that is planned for a family meal, or not all of the snacks, just a reasonable amount, or whatever.
You and your wife are presumably fighting, not because of your children (don't blame it on them!), but because of the extreme and unreasonable rigidity you're trying to impose on them, and her having a more reasonable view.
If you love your family, this is not a reasonable way to be. Look inside yourself, is this from your own childhood and your parents were unreasonably strict? Where is this need to control coming from? And how do you work on it to relax and let all the members of your family feel safe and relaxed in their own home? Because you're not allowing that at the moment.
Along with all the other posters here, I believe it's you who needs to change on this.