Well, Gran this actually helps you out, as far as knowing what to do with the 6 y/o for part of each day - you are going to run a cooking school. May have to wait for nap time with the baby. Pick something healthy-ish and have him "learn to make it". Kids tend to at least try what they have had a hand in making. At 6, no knives though because if he cuts himself, he will not be in the kitchen again for a long time, AND you will look like an awful babysitter. Pushing the button on a food processor however is BIG time fun for a 6 y/o though. Start with something gooshy is always fun. My youngest has her "own" recipe for guacamole and loves mashing it up with a fork and sprinking in the spices to her own taste. And then she eats it. Yogurt smoothies where the kid can choose his own fruit, juice or milk, and flavor of yogurt and gets to blend it himself and drink it through a colored straw makes good snacks or breakfast.
Try websites like Familyfun.com for ideas and the libraries have kids cookbooks. Hands on food where he gets to make his own choices, so it is "his". Food with funny names help too - my youngest will eat toad in a hole (fried egg cooked in the center of a piece of bread), but not toast with egg. Have him help and watch you in the kitchen as much as possible. "Forget" to buy some of the junk on the list, but have some of it in case he goes on strike. Look for healthier alternatives to some of it, if possible. Keep it where he cannot see it, so he does not remember it.
Teach him to make "cowboy food" if they are not already from Texas, i.e. cornbread cooked in a skillet, very mild chili, have him help you roll up cheese enchilladas,etc.
A benefit is he may take this knowledge home and show his mom what he can make, and continue the new expanded diet. He wont like everything he makes, but if he tries one new thing a day, wonderful. He may have the healthiest diet of his life for one week. What is the baby eating this week? You have a great opportunity!