If he's a year old, he really doesn't need cow's milk. In fact, humans are not designed to digest cow's milk and humans are the only mammals that consume the milk of another mammal.
Also, it sounds like he's allergic (and not just lactose intolerant), particularly since he hasn't taken to yogurt or cheese. The vomiting was my oldest son's reaction to dairy and while he did have dairy when he was 7-10 years old (he seemed to tolerate it then), we found out at age 10 that he was still really allergic (although no outward symptoms). Soy milk isn't a great alternative as the health benefits are way over-rated and if you research you can find that processed soy (not fermented soy, which is okay and what the Japanese eat) is really bad for the thyroid.
There is rice milk that is fortified with the vitamins that are found in cow's milk - that tends to be more palatable than soy. And, there's also a potato milk.
Also, here's a list of non-dairy foods that are great calcium sources:
http://tinyurl.com/5fevw5
If he won't eat the veggies outright, them process them in the food processor and make him turkey meatloaf or meatballs.
Also, blackstrap molasses is very high in calcium and is a really good sugar alternative when baking. The other top things are beans like navy beans and figs, with the latter being something your son might not like, but you can grind up figs in the food processor and add them to baked goods.
Also, you need to remember that for kids this age, a serving of food is really quite small (I'm remembering a tbsp per year of age for toddlers), so he might be getting enough. If you're really worried, take him in for regular weight checks at the pediatrician - there should be no charge for that.
Also, while this is a hassle right now, in the end, your child will likely be a healthier eater and much healthier overall - that's been the case with my kids in having to pay special attention to their diet.
