Wow...what an attitude that dietician has! Hopefully I can help.
Here's a link to a site with calcium rich foods you can eat. I'm not sure how much you would need to eat on a daily basis to make sure you get your daily's worth, but perhaps a smaller supplement amount would be needed if you can include these items in your daily diet. http://www.citracal.com/Calcium/Foods/Vegetables.aspx You do NOT need to drink milk to get calcium. Although, you CAN get soy milk that is fortified with calcium.
As for getting the rest of your daily nutrients, I would say to make sure that you are eating 5 servings of fruits and vegetables per day. Here's a little bit of info about serving sizes of fruits and vegetables: http://nutrition.about.com/od/fruitsandvegetables/f/servingfruit.htm
As for meats or proteins, here are some suggestions for protein intake and portion sizes to get enough protein for the day: http://www.everydiet.org/999/protein-benefits
As for your fiber intake, you can get fiber from these non-gluten-based sources (there are 6 pages, all will some fiber ideas for your daily intake...and some can be combined with your fruit/veggie intake as well. :) http://celiacdisease.about.com/od/theglutenfreediet/ss/HighFiber.htm
Definitely stay away from the potato chips, except as a snack on occasion. There are LOTS of products and brands that you can buy from your regular grocery store that are gluten-free. Hellmanns Mayo is gluten-free (although I don't know if they are milk free). There's a product out there called Vegenaise that is supposed to be mayo that is completely vegan, which would rule out the milk or eggs. Check with your grocer to see if they carry it or would be willing to stock it. I know that sometimes stores will cater to people's vegan diets in a natural foods section, so maybe your grocer would stock it to cater to those people. Heinz Ketchup is gluten-free as is French's mustard. Most of your fruits, veggies, plain meats (with nothing added - chicken, beef, pork, turkey) are all safe to get from your local grocery store. You can buy plain rice, Betty Crocker's Instant Mashed Potato (Potato Buds) - the PLAIN kind...not the flavored ones - as some alternatives. You can even buy cereal at your regular grocery store. Most versions of Chex are now gluten-free! Rice, Corn, Cinnamon, Chocolate, and Strawberry Chex are gluten-free. So, you could even have a few options of flavors to choose from! If you need to occasionally have some sweets, you can check out Betty Crocker's gluten-free cake, brownie, and cookie mixes. I'm not sure whether they contain milk products, but you can check it out and see. Most stores carry their products and they would be right in the regular cake mix aisle. If you can find a place that you can get some rice or corn based pasta without having to travel 50 miles, that would be a great way to substitute pasta in certain dishes. We do spaghetti here at our house and you can't tell the difference. You can use Hunts brand spaghetti sauce (although stay away from Hunts brand Ketchup...that apparently isn't gluten-free). You could even make your own meatballs using some gluten-free bread crumbs (or crumbling up gluten-free bread).
Definitely try to buy as fresh as you can to get the proper dietary intake of your nutrients, but if you need to, you can do as I've been doing and take a daily multi-vitamin and a daily calcium supplement (list of all gluten-free supplements and drugs are listed here: http://www.glutenfreedrugs.com/list.htm ). That way you care covered on anything you might not get on a daily basis, but you can try your best to get most of your daily intake of vitamins the natural way through your fresh foods.
If there's anything else you need help with, let me know. Hopefully this is more helpful than the dietician! I know it's a lot of extra reading for you, but hopefully it will give you an idea of what will and won't help you get the dietary intake that you need.