We went through this with Joey, during a food switch he became really fussy, and I gave him a little chicken and rice, and he ate out the chicken. A couple of things to remember is that they go through growing spurts, and some days they are hungrier than others. Once you feed them something that tastes really good, they will hold out for something that is just as good. The same is true with children, you have to be stronger willed than they are. This is harder when the dog is really small, or might be susceptible to hypoglycemia, so familiarize yourself with the symptoms.
Toy Breed Hypoglycemia
I think home cooking is great, and some dog's really have little choice because of food allergies or special needs, but it can be very time consuming, if you do it right. If you are happy with the food you are using, you can do several things to help him eat. Some people pour a little parmesan cheese on top, and dogs love the smell so this will entice them, others will hand feed a few pieces. If the wet food that he vomited was a new food, this often happens, so many people will just put a tsp or so on the kibble, go slowly when you introduce new foods. Some dogs that really love their food, will often eat so fast that they vomit and then eat that, so in a way, it's kind of good if there are not nuts about their food. I would avoid giving him human foods for a while, and if you decide to give him some chicken or something, I would do it after his meal, and only a tiny piece as a treat. In this way, you won't be making him too fussy.
By the way Ellie May is our homecooking expert and highly recommends it, but never glosses over the disadvantages such as time and expense. I think if you decide to do it you have to be highly motivated because it will be difficult to change back.