I am a naturopathic doctor in Nashua New Hampshire and deal with these issues all the time in my medical practice, and at home with my own child. I would be more than happy to talk to you at some point if you like.
I don't know your children's medical history, but there are so many whole foods options for children. One thing I can tell you that has really worked in changing the diet for my daughter is to get on board with her, and eat what she eats. So if you remove gluten or dairy for them, I think it is helpful to do it for yourself. It creates solidarity with the family, cuts down on the time you need to cook, and in many cases if a child is experiencing issues, it is often the case that the parents have a problem with the same foods.
I am not sure why your doctor encouraged the vegetarian piece. I think vegetables should be at the heart of their nutrition, but good quality, meat, fish and eggs are wonderful foods for children, and in my medical practice I see that children who eat animal protein seems to be healthier.
If you have a health food store in your area, I would suggest giving a call to them and ask them if they would be willing to give you a tour of their gluten free and dairy free groceries. I know that Whole Foods would be helpful with something like this. There are so many great rice crackers, gluten free snack including cookies, gluten free baking flours, and gluten free and dairy free chicken nuggets. Even a more conventional store like Hannafords has a decent Gluten Free section.
However, what has worked for me with my own child, is to prepare a healthy meal, and start eating. Also, get your children involved in some way with the cooking. If your children tell you they don't like it, let them know that this is what you have prepared for dinner, and I can assure they will eat. Most of the time, children will eat when they are hungry. I have found that limiting choices actually works.
As for a book, I hope to be the person who writes it, stay tuned.
All the best,