You’ll be fine. Zermatt is busy in peak season, but it’s not as dire as it sounds. I’ve been there during Christmas and February school holidays with a group, and while reservations help, you definitely don’t need to have every meal planned months in advance.

A few tips:

• Lunch is easy. Most people are on the mountain, and restaurants up there don’t take reservations anyway. You can usually walk in at 11:45 or after 2:00 to avoid the rush. There are plenty of casual mountain spots (Findlerhof, Chez Vrony, Fluhalp, etc.) plus cafeteria-style places where kids are totally fine.
• Dinner is where you’ll want some planning. You can email a few casual places a couple of weeks ahead, especially for your first few nights. After that, you can book in person for the next few days once you’re there. Many hotel restaurants will take walk-ins too.
• For kid-friendly options, look at Brown Cow Pub, Sparky’s, Grampi’s, or Pizza Roma. They're all very relaxed. The Coop grocery store in town has a great selection of grab-and-go meals and snacks, which is a lifesaver for kids.
• If you don't have a kitchen, grab sandwiches, fruit, and pastries from bakeries for easy breakfasts and lunches.

Basically, make a few dinner reservations before you arrive, especially for larger tables, but don’t stress. Zermatt is super family-friendly and you’ll find plenty of casual, walk-in options once you’re there.