Bought a house with a newer hot water heater (less than 5yrs old). The shower would never get very hot and would quickly run out of hot water completely (7-12 mintues). We replaced the cartridge inside the single handle valve and still had the issue. Plumber came out and said it was most likely build up from hot water so we replaced the tank just last month (55 gal for a home for 2 adults). Got the new tank - same issue. Husband turned up the water temperature - same issue. If we run the washing machine or dishwasher - forget it. No hot water for hours. 

The handle valve is inconsistent. Sometimes you turn it all the way right and the water only ever gets warm, not hot. We found that if you turn it hard to the right, the water will get scolding hot and then when turning it down it just stays scolding hot where the water was previously ice cold. It's not until you almost turn it off that the water gets cold, then it stays cold for a minute or two and doesn't get hot until almost all the way to the right. The water doesn't seem to run out and we can fully shower now with hot water. It's a pain to mess with it everyday. 

Any ideas what the issue is? We also replaced the faucet head. There's no issue with getting hot water anywhere else. The only difference we've seen since the new hot water tank is that the sink fuacets don't get as hot as they used to and just adding a little bit of cold water makes it freezing.