Hello, if your line has a break on the exterior of the house you would not have any pressure at all in either hot or cold. Plus the water would be a break that would bubble up through the ground, and the city is usually on those pretty quick.

You say you went through 3 faucets, if you had an exterior sentiment mixing with your everyday water you would also have changed out 3 water heaters. So that tells me that the issue is between your water heater and your kitchen faucet. If you had the issue before the water was entering the house you would have also changed out 3 shower faucets as well.

What this tells me is that you have a waterline most likely on the hot side only that is plumbed in piping that is other than copper or CPVC. Check the hot water line coming off your water heater and see if you have black pipe somewhere on the way to the kitchen sink. Black pipe is used for gas lines only, and will rust. What you are most likely experiencing is a pipe rusting out from the inside out. Hope this helps

Sincerely Andy