I am typically the first one in my house to take a shower and I like hot showers. I have noticed that if I take a shower first, the hot water is not that hot and doesn’t last very long. But if others take showers before me and the hot water has to recharge then the hot water is HOT and lasts a long time.
I have a 50 gallon hot water tank.
The only two things I have (besides sinks and showers) that use hot water are a dumb dishwasher and a dumb washing machine.
What I was thinking was to set up an automation in HA to somehow trigger something to use hot water for like 10 minutes in order to get the hot water heater to recharge.
Any ideas?
I would bet that the thermostat in your water heater is faulty, and has a hysteresis value that is too strong.
The heater is supposed to switch on when the water temperature goes below a certain value, and switch back off when the temperature goes above a certain value. Those temperatures should be close enough, so the temperature is almost constant; but not too close, so the heater does not switch on and off constantly.
In your heater, those two values are way too far apart. When the heater is idle, it allows the water to get warm. When someone takes a shower, the temperature decreases, then it finally switches the heater on. And it does not switch the heater off until the water is hot.