A meal at V&A's takes three hours. I can't imagine a a 6 year old and a 9 year old being able to sit through it quietly. I was just at Disney World last week with two 9 year olds and they would have been miserable at V&A's. There is no children's menu, no crayons, nothing like there is at all the other WDW restaurants. Children would not like the food.
We've dinned at V&A numerous times and have never seen a child there. I would suggest that if you and your mother want to eat there, you should leave the children in the children's club at the GF for the evening. Dress is jackets for men and cocktail dresses, etc. for ladies.
They usually have seatings clustered around 6 p.m. and another set of seatings clustered around 9 p.m. If you do the 9 p.m. do it on an evening when you're not too tired. We've done both and prefer the earlier seating. The evening after spa treatments sounds like a great idea -- very heavenly.
Also, since you're on the Platinum Plan, you've essentially already paid for dinner at V&A, so you shouldn't miss it!
Ideas for dinner on the Platinum Plan with children -- Character Dinner at Garden Grill, Morocco (live entertainment including a belly dancer who brings kids up to dance with her) Mexico (not the greatest food, but great atmosphere that kids would like), Italy, Chef's de France, Boma at AKL, Cinderella's Royal Table for breakfast, lunch or dinner, Sci Fi Dine In, Prime Time Cafe, Rainforest Cafe, Mama Melrose, Coral Reef, Ice Cream Social at Garden Grill.
As for more upscale restaurants, California Grill usually has lots of kids due to the fireworks. We've seen children at Citrico's, Narcoosie's, Flying Fish Cafe, Artist Point and Jiko, although quite frankly the children we've seen at these restaurants always look tired and bored (or they've already fallen asleep in their seats!).
I hate to say it since you're obviously very excited about the Platinum Plan, but you may want to consider whether, with two children, it makes sense to do that or to go with a simpler package and pay for the nice things you want to do. Up to you, of course, but I think children somewhat limit your ability to take advantage of some of the package items. I say that from experience having gone to WDW many times with children and just with DH and me. It's a different vacation with children and generally far less "upscale".