I've experienced this one. I agree that you shouldn't fix a separate meal for her. I also agree that she should sit down to dinner with you. If she chooses not to eat she still won't get that pb&j sandwich.
One of the reasons that I say this is my daughter came to me as a foster child and she refused to eat almost everything I cooked. We were dealing with a lot of more serious emotional issues and I let that one slide. We usually had fast food after I picked her up after work. She became an overweight child and still battles with her weight. The pediatrician told me at the time that I was doing her a disservice because she was not getting the nutrition that she needed and that once a child puts on fat it's extremely difficult to get it off. I was overwhelmed and didn't follow thru with a better diet.
I think my daughter learned a positive lesson from my negative example. She fixes her children nutritious meals. Everyone sits at the table and everyone eats (or not) what is on the table. She doesn't treat it as a "big deal." It's just the way it is.
Her 4yo son has become a picky eater and he frequently doesn't eat the three bites of each food that she requires. He later says he's hungry. She offers him the rest of his meal which he sometimes accepts. He likes fruit. That is usully his other choice but he frequently refuses it in the evening. So....he goes to bed still saying he's hungry. This has been going on for about a month now and more and more often he either finishes his dinner at dinner time or finishes it later. He may not be ready to eat at the same time his mother and sister are. By providing him the opportunity to eat it later he has the healthy option of eating when he's hungry.
I think with my grandson is going thru a phase and I can see how it would be easier to let a child eat whatever they want. I did it. It is not easier in the long run. This issue with food is not only about food but also about teaching healthy eating habits and ways to interact with family. For me and possibly you the lesson is about learning to take care of ourselves. Fixing a separate meal uses time and energy not to mention frustration. In the long run having one meal that everyone eats (or not) creates a more cohesive family and a mother who will have more time for something fun.
One idea is to tell her that you would really like to play a game with her, watch a little TV with her, or whatever she enjoys doing but you haven't had time to do. You are probably also not in the mood when there's a hassle over food. Give her a choice of eating at least part of her meal and then spend 15-30 minutes with her as exclusively as you can. Perhaps she could stay "up" 15 minutes longer than her brother so that you can cuddle with her or read a second story.
My daughter does ask the kids what they want when she has time to do so. However she gives them choices not an open ended question. "Would you like chicken or a hamburger patty." If she has hamburger she may ask if they want a patty or noodles with hamburger and a sauce. (She has a name for it.)
She has one of the children set the table. Sometimes she has a simple desert that requires finishing the meal.
If her son refuses to eat she sends him to his room until they've finished eating. I've been there when he comes back to the table and starts eating in just a few minutes.
I believe she is successful because her attitude is a matter of fact, "this is the way it is." If you choose to not eat with us you may go to your room." (play is OK. It's not a punishment.)
" Come back when you're ready to eat."
Another idea is to have your daughter choose two (or how many you want) foods that she doesn't have to eat. But no peanut butter sandwiches until she's eaten a part of her dinner at the same time as the rest of the family. And even then she cannot make the sandwich until everyone else is thru eating.
I remember having meal time turn into a power struggle with my daughter. "You will sit at the table now." "No, I won't!" That doesn't work. Neither of us won. The situation has to be win-win for both of you. She may not feel that she can win because she can only see what she wants. Over time, and with increased maturity, she'll have learned some of what makes a win-win situation.
Be patient. It takes time to retrain everyone.