This is familiar! Every family is different. Here’s how we make it work with 11 of us, one very picky (almost no meat, no pasta, no rice, etc).
Meals happen at 7am, noon, and 5pm. I make a meal and you eat it or not. But you don’t get anything else. We do require older kids (age 5+) to take a couple small bites of things they don’t like before they can take seconds on things they DO like.
Snacks are spaced between meals at 10am, 3pm, and 7pm. You may eat what I offer at this time. Snacks are small and generally we offer: fruit, veggies, or pretzels. Sometimes I have homemade granola bars, crackers and peanut butter, or nuts. Dried fruit is also sometimes available at snack time. All snack items have portion sizes – kids know to use a specific measuring cup for pretzels, etc. I do allow lots of veggies if they want them, but fruits generally are limited to one serving.
Nobody grabs food outside of these specific times, parents included.
I don’t insist anyone eats, but I also don’t let them eat junk food between meals. We drink water. Milk occasionally (like with pancakes or on cereal). Generally, the kids eat at least some of what is offered. It is very rare to have someone totally pass up all food at a meal. They will usually eat at least the fruit offered.
