ETA: I think you have two different problems with the complaining and the grazing. I would suggest working on one or the other, but not both at the same time. If you want her to stay at the table, strategize with your spouse to ignore the unpleasant complaining. If you want to correct the complaining, then let her graze. I don't think there's a way to do both, immediately, and get a good lasting result. The ante gets upped too much. Just my opinion.
Hi DVMMOM,
Did your child just start kindergarten this year? Sometimes, the highly structured day is hard for kids to adjust to, and being picky about something or another may be a way of gaining control of things. The fact that she's having a hard time sitting still may be a response to being at a desk and being indoors for much of the day.
One thing we have done at home is to tell our son (also five, also just started kindy) that he needs to sit at the table until he's done eating, period. The only exception is going to the bathroom. I would suggest telling your daughter that she needs to sit at the table until the dessert if she wants some. This means that she needs to sit with you and, eating or not, stay at the table. Chances are, she'll take a few more bites of her dinner.
I would ignore the complaining, if it were me. I find that even talking to my son about the complaining only seems to keep it present. I instead try to focus on other subjects, and positively notice "Wow! You ate all the carrots." (Granted, I only have one child, so this complaining is easy to ignore.) I understand the meat-needs-ketchup and other sorts of things, and whatever is easily accommodated, I'd let go of. If it's extra work, let her help prepare it. She's old enough to get things for herself in the kitchen.
Kids do chat chat chat at the table. When I was teaching preschool, it was easier to make sure that kids were tucking into their lunches; it's harder for the teachers to do that without completely separating her. She is going to have to learn to eat at that time, eventually. However, even if she was eating a full lunch, kids at this age are often still hungry at 2-3 and still need an afternoon snack of a good protein and carbohydrate.
Overall, what's worked for us is not giving in to 'I'm hungry' between meals and snacks. So, when it's bedtime and Kiddo kind of blew it at dinner and didn't eat much, he'll complain that he's hungry and ask for something to eat. I tell him that the he'll get to have a great breakfast in the morning, at breakfast time. Dinnertime was the time to eat. This has worked best for us. NOT getting him a before-bed meal.
By the way, we do our desserts at 3 or so, a few times a week, because I don't like to connect it to 'eat your dinner', and we don't have super-sweet desserts, so that is a non-issue. I don't know if that will help, but it works better for us this way. That way, dinner is its own entity and when it's done, it's done. If you are willing to move dessert time, it might make things easier. This way, if it's a control issue, she can get up and leave and have her clear her place before she goes to play, but be very firm that when she leaves, she's done. No coming back because she's hungry again.