I don't personally think your kids are old enough to cut out meat and dairy from their diets. They are getting essential fats, omegas, and proteins that can't be replaced in high enough quantities at their ages.
I also have 2 kids, 2 and 4. I am a vegetarian - technically a pescetarian because I eat fish but no poultry or meat. Anyway I cook 2 dinners every night. It's not as hard as it might sound.
I want my kids to have meat and dairy in their diets...later on in life if they choose to become vegetarians, that will be their choice, not mine. As for my husband, he LOVES meat but also loves that we eat healthy. So for the kids, who are hungry somewhere around 5-5:30, I make a protein (hamburger, grilled chicken, meatballs, sausage, fish sticks), then make a carb - pasta, grilled cheese, farro (google this if you haven't used it before - it's a grain that tastes like brown rice...TONS of health benefits and my kids love it), corn...we consider that a carb. :) Then we do a veggie - peas, broccoli, tomatoes, edamame, whatever I have on hand. The kicker is that on my days off work I roast squashes, beans, and eggplants and puree them & throw them into the freezer in serving portions. I put a serving of roasted veggies into almost any dinner I make for my kids. Orange squash puree into homemade pizza sauce, acorn squash puree into Annie's white shells & cheese, roasted beets into a strawberry-banana smoothie. You get the idea. Therefore you can continue serving some kid-friendly foods which are actually heartily fortified with veggies.
For my husband and I, we do a salad about 4 nights a week. Escarole or arugula or other salad greens, dry roasted walnuts, fresh dill, chopped tomatoes and radishes, whatever else you like. Good enough to eat almost every night. Then we'll throw fish on the grill, or I'll make a yummy sauce for some pasta or risotto, and I'll saute kale or roast broccoli, cauliflower or squash (try delicata squash with fresh garlic and shredded parmesan, roasted until golden brown then deglaze the dish with dry white wine when it comes out of the oven). My husband and I don't eat until 7:30 or so, but we don't mind because it's a peaceful meal, just the 2 of us.
I was vegetarian for 12 years before I got pregnant with my 1st baby...I started eating meat again during that pregnancy, and ate meat all the way until I was finished nursing my 2nd one. Back in June of this year I quit eating meat totally again (except for fish). I had my cholesterol and full bloodwork done back in March...then I had it done again in Sept because we applied for life ins. My overall cholesterol number dropped 12 points, and it was all LDL. Also my triglycerides decreased by 13 points. Pretty significant.