hooeey! Hot thread!
Ok, here's how it goes down in my house. When you're over my house, you don't have to eat what I cook, but you're not getting anything else, either.
I am not a short order cook.
I'm not going to force you to eat
anything, but you don't get to forage in my pantry if you decide my dinner stinks.
If the family is doing a dessert that night, then I need the kids to eat at least the protein and the veggies. I don't care if they don't eat the starch-but if you want dessert, then you need to eat the protein and the veggies. If you
choose not to eat those two items, then you don't get dessert.
No dessert is not going to kill you.

And like many things in life, sometimes you have to get past the unpleasant things (like brussell sprouts) to get to the rewards.
I also let the kids put their own portions on the plate-you may hate the spinach salad, but you're also deciding (within reason) how much of it you want to eat.
There are no battles in our household over food-there IS whining about desserts, but I expect that. I say, you know the rules, it's your choice what you eat.
To the OP, I think she outsmarted you in the food battle department; chalk it up to a learning experience and figure out how to make dinner a happier experience next time.