Sudden stop of wet food diet is causing my cat to vomit

Firstly, free feeding dry food is the fastest way to turn any cat into an overweight cat. Your vet's advice is wildly wrong in this case. Hill's (a respected pet food company) has this to say:

Free feeding cats can lead to overeating and obesity. It can also be difficult to tell if your cat's appetite has changed, for the better or worse. It's also difficult to tell, if you have multiple cats, how much each one is eating.

(source: Meal Feeding vs. Free Feeding Cats: What's Best?, emphasis mine)

The idea that wet food is "unhealthy," "a treat," or otherwise bad for cats is an older belief that more vets are beginning to leave behind, but some older vets still hold on to that belief. Free feeding kibble is the old, and honestly lazy, way of caring for a cat, and has led to large numbers of overweight pet cats. From Global Pet Foods:

Free feeding makes it easy for indoor cats to consume more calories than they are expending, leading to weight gain and possible obesity.

(Source: Is free feeding your cat the best option?)

Secondly, simply looking at weight isn't a good way for anyone to determine the body condition of your cat. Please reference my answer on "How can I measure the weight of my cat?" for the appropriate way to determine if your cat does in fact need to lose weight, as well as an explanation of why pure weight isn't a sufficient metric to use.

Thirdly, simply looking at the quantity of food being offered isn't a way to determine if your cat is getting the right amount; each brand and flavor will have a different calorie (kCal) content, and just like in humans, calories are what's important for weight gain, loss, and maintenance. According to All Feline Hospital:

The average indoor cat should have 20 calories per pound to maintain weight. The average outdoor only cat should have 35 calories per pound to maintain weight. Indoor/outdoor cats are somewhere in between.

(Source: Getting Your Cat to Lose Weight)

You also can't cut their food too drastically; from the same link above, "If your cat is overweight, you will want to feed for 2 pounds less, or 40 fewer calories a day, and readjust every time your cat loses a pound, until you hit a healthy weight, and then maintain." An extreme drop in calories, particularly with an overweight cat, can cause hepatic lipidosis, also known as "fatty liver disease," a fatal condition.

Cats will naturally eat a number of smaller meals, which is very similar to their wild behavior; cats have not been domesticated all that long in the grand scheme of the species, and still retain most of their wild traits, including frequent small meals and getting most of their water from food. Because of the water content, wet food is actually more filling than dry to them; this may be part of why your cat is vomiting, as well. He may be eating a similar physical quantity, but as the food absorbs moisture in his stomach, it swells and causes him to vomit.

I would advise the opinion of a second vet, as the advice to move "fat" cats to a feeding pattern that is well known to encourage feline obesity is not good. Check their condition yourself using the touch-test linked previously, and find a different vet for additional consultation about their body condition and caloric needs. I would also advise returning to their original diet and schedule for now.