New faucet likely won't help..However.. Things to consider.
On most RV's they recommend a pressure regulator, 45PSI, be installed, Some have one built in (usually a Sure-Flo) but many buy a small brass cylinder with hose fittings on each end, the cylinder is about the size of a female hose connector.. These come in two types.. Regular, which is junk and you should forget them, they restrict the flow of water, and "High Volume" or "high Capacity" which has a colored plastic grip on the female end.. I give these a 9 on the 10 scale (They are ALMOST good enough) The Sure-Flo in-line gets a 9.9 or better (Read that passes enough water for a nice shower)
The next thing is water filters.. Now I don't know about you but I find the water at many parks to be kind of ... Needing filtering... So I have filters.. These will reduce the pressure as much as 10PSI so if I put my regulator in front of the filter I have only 35, not 45 PSI at the rig and not nearly enough water for that shower.. So I use two regulators... (If needed) one pre-filter set to 60-70 PSI and noe post filter (The Sure-Flow) set to 45.. The Pre filter is a Watts.. Both Watts and Valterra make very good regulators, these are in the Plumbing department and come with pipe fittings, not hose fittings (You can get adapters near by, same dept)
Avoid the smallest model, anything else is good.
Finally: If it's a shower that's runnign slow.. Many folks put a "Flow Restrictor" washer behind the shower head.. This is a flat metal washer usually with a quarter inch or smaller hole in it.. Frankly.. I can pass water faster than it can (if you get my drift) and the best thing you can do if you want a nice shower is remove it. As for kitchen faucets.. I've not seen one there....yet.
Home is where I park it!