Some appliances are designed to be used when you are plugged into shore power, or while using a generator. I am impressed with the inverter, if it is allowing that load with the electric heater. Of course, that is what is drawing the battery down: you are using amps faster than you can replenish them. You may want to do an electrical "inventory" to see how many amps each of your appliances actually use. With the 30 amp system we had in our boat, we could not run the water heater and an electric heater at the same time. You have to learn to prioritize what electric draws you can use at the same time, according to whether you are on shore power or the inverter. Going to run the microwave? Turn off the electric heater, even when plugged in. Water heater? Yep, unplug the electric heater. Your wife is going to use a hair dryer? Well, you get the idea.
The R23 is a very capable boat with a lot of amenities. If you haven't had to adjust to "power management," this is a good time to learn. Same is true with many RVs. Or, homes that are off the grid. It isn't a problem with the boat, just something that needs to be learned and put into practice.
