When I turn on the kitchen hot water, it heats up, then rattles, and the pressure cuts back by at least 50%. This does not happen with the dishwasher or the cold water. Any suggestions?
If you're only opening it just a bit, then it can be thermal expansion. When the hot water reaches the valve, it can cause some component to lengthen slightly, closing the valve a bit more than it was.
I've seen that exact behavior on bathtub valves as well. If the behavior is new, it could be that a washer is staying compressed when cold and is expanding only when it gets warm. If so, replacing the washer may change it up.
Does it cut back 50% if you open the valve all the way, or only if you open it a "normal" amount?
The faucet needs rebuilding with a re-build kit specifically for the faucet, some faucet's rubber seats collapse as they fail & dramatically reduce flow.
The other possibility is that a piece of large debris got caught within the faucet & only releases to block the flow with hot water. This may be successfully back-washed out, but usually the faucet has to be replaced.
If it's not an older house with screw-retained compression washers (the screw heads can rot out & fall into the house piping to end up in faucets), then debris of this size could indicate interior pipe corrosion or that piping valves & Shut-Offs are built-up with water deposits & both should be operated to scrape-off or break-off any build-up.