You can always eat what you want. That said, if you want to give this a real try and see how you really feel, then tell your family that you're going to do this. They can either get on board for the one month test or they can make their own food. Eleven years old is old enough to learn how to make one meal a day if need be, and they'll be better off in life knowing how to prepare food. Otherwise, they can get on board for a 30 day test period. That's my two cents, but I live in a crazy world where we support each other on endeavors that will improve health and well being.

Now, I'm always concerned about young kids being vegetarians. At that age there is a serious need for a good supply of good fats for proper brain development. Is this the child's choice? Have they sat down and explained to you exactly how they plan to get their supply of the fats they need for proper brain development? What about important fat soluble vitamins like K2? If they can make a plan let them keep on the diet, otherwise it's time for change.

Now most kids do not like most vegetables and Mark over at MDA has done posts on this including what the current science says about why. Children not liking any animal meat is very rare.

Onto the paleo/primal.... Yes, no grains. Especially not corn (polenta). Potatoes are not a grain and there is a real divide in the community regarding their edibility while paleo. I'm on the side of without skin and cooked, and they'll be great source of carbohydrate for a growing eleven year old. Avoid all the gluten free substitutes that are just grains safe for a celiac but still have a lot of health issues due to the proteins in them.

Keep the meals simple. Cook one meat/fish, one vegetable and one root (potato, sweet potato, squash, etc.). Weeknights make it simple. One the weekend you can cook a roast or make a stew that you can spread out for lunches. And nothing is easier than bacon and eggs in the morning. Bacon in a 450F oven for 8-15 minutes (depends on thickness and desired doneness) and cook the eggs the way you guys like. You can even make up a bunch of roasted potatoes on the weekend to warm up while cooking the bacon.

Stews are easy... And they are damn tasty. Learn how to make a stock (bone broth) Use that along with a cheap roast (chuck, rump, etc) some vegetables, fruit and spices. The combinations are endless really.

Pick up a pate and dehydrated fruit to use in place for bread. Apple crisps, pear crisps, etc. It's a quick and very nutritious meal. Get a duck liver mousse with cognac. Delicious.

If you're craving pasta I've found that celery root (celeriac) works amazing with pestos and marinaras. You can even use it to make a lasagna.

Also, kids will not starve. They'll eat eventually, just don't force the issue. If he doesn't want to eat what is there it's okay. Also, you cannot control what he eats outside of the home and don't make a big deal if he's getting mcdonalds, dominos, etc.

Allow a cheat day for the family. You can abstain, but allow them to have something on a Saturday night.

If you make the food really tasty, they'll jump right on board. Get a copy of NomNomPaleo and work from that. Use MDA for some very easy quick recipes. Change things up.

My husband isn't interested in eating like me. I just make modifications. I'll have the meat and veg and skip the white stuff(rice, potatoes,etc). I'll put marinara sauce over cauliflower or zoodles. Pulled pork goes over a sweet potato instead of a bun. Doesn't take much extra work or money. You got this!

I cook dinner for everyone that *I* can eat (meat, poultry, fish and veggies) and then add in starches (rice, pasta, potatoes) for the rest of the family. That way I'm cooking one meal, but I'm just not eating the starch course -- or if I'm needing more calories, I'll just pop a sweet potato in the oven for myself, as it's not that much extra effort. I also keep food in the house that my picky eater can fix for herself.

I was on Paleo once and failed because I always got the third degree about the food budget because nobody else wanted to eat like me. I failed badly because of this.

This year my wife hopped on board, she still has a little milk with the paleo crunch I make and a yogurt for lunch. But she gave up all grains and processed meals so that was huge.

Either the kids eat what I cook or they get their own. They are 11 and 13 now so no more dual meals in the house this year. My son is about 50/50 with us and my daughter has had her own diet for years, very picky. I am open to just about anything. I love food so making new stuff is fun.

What an amazing amount of ideas you have here!

We have a very similar situation except not vegetarian, and for dinner we have some variation of meat/fish/chicken and salad/veg most nights of the week. Its amazing how varied meals can be using that template. I do eat potato which helps. Eggs for dinner pretty regularly too. Maybe you could feed your son some vege patties etc with the salad/veg

If everyone else is having pasta I will generally microwave myself a small sweet potato instead. Only takes 4 mins and no prep.

There are plenty of tasty options that can be alternatives to grains at the dinner table, such as: zucchini noodles, spaghetti squash, cauliflower "rice", no grain-ola, etc... My husband usually gets his bread meals when he eats out for lunch and is happy to have less of it at home. If my son doesn't want any of the dinner I make, there is always cheese, applesauce, yogurt, and fruits.
I decided to become vegetarian when I was 10 and was until I was 20. I was anemic, so not sure it was all that great for my health. I eat way more vegetables now, than I ever did as a vegetarian!

I generally make something with meat & veg and add starch for the kids. I eat low carb - they don't need to be that, especially since they're not with us all the time. If I cook quiche, I'll make a separate pan for mine because I can't tolerate regular eggs, so if there's some potatoes or rice in the fridge it gets added to theirs. If I make something casserole-y, I leave out the starches and let them just dump it over rice or a baked potato. Stir fry style is easy. So is grilling. Try to figure out meals where you can serve pieces to whoever wants them instead of 1 mixed dish for everyone.