Thanks for all the encouragement and advice regarding Kate's dinnertime habits. I don't think I'll go with the "sit here until all those peas are gone!" thing (no one seriously suggested that--more like cautionary tales from one's own childhood), but I'll definitely continue to offer them and not try to supplement with extra fruit.
Regarding the sitting-down-to-eat thing, I had been feeling it was time to get stricter on that anyway, so we laid down the law on that one last night. We were having pasta--something Kate likes almost as much as we do--so fortunately we could focus on the sitting and not so much on the food. (Yes, yesterday was our anniversary, but our nice date will be tonight, so we just had our favorite Italian meal last night at home.) Anyway, Kate managed to stay strapped into her seat for the whole meal, so in a way that was easier than I expected. She screamed and squirmed off and on--and was generally too frustrated to eat more than a few pieces of pasta and the tomatoes out of her salad--but that's all fine. Tonight she'll be with Granna and Opa, and never has trouble staying in her seat there or at school, but we'll see how it goes Saturday and Sunday at home again!
On to the next fun parenting challenge I can pick your brain about: potty training!!