You didn't mention the age of your current gas-fired water heater. Since it does not always provide adequate hot water I am going to assume it is more than 10-years-old.
- Unless you have been diligent in periodically drawing water from the bottom of your water heater you most likely have a buildup of mineral deposits in the tank which increases the recovery time to reheat the water in the tank.
- The mineral deposits act as an insulator reducing the amount of heat from the gas flame from reaching the water in the bottom of the tank. As this condition worsens you may even be able to hear the water heater "gurgle" as steam bubbles are released from the mineral deposits in the bottom of the tank.
- If your plumber cannot clean these deposits or if your tank is beyond designed service life it may be time for a replacement.
Tankless water heaters are higher in efficiency (EF 80 - 96) when compared to tank water heaters (EF 54 - 64). Tankless are also much more expensive to purchase and install.
- Older homes may require gas line improvements to ensure adequate gas supply to a new tankless system.
- The greatest advantage is an endless supply of hot water which might not be as important to you and your mother since you hot water needs may be rather minimal when compared to a house full of teenagers.
The only fixture that may require an abnormally high amount of hot water is the step in bathtub. If it requires more hot water than can be provided by a traditional high efficiency water heater, you may be a candidate for a tankless system.
My experience is that households with your demographics cannot normally justify the added expense of a tankless system.
- You might better invest in a high efficiency water heater tank system and reduce your lavatory sink and shower loads by installing reduced flow fixtures.
- When replacing your dishwasher install a unit that uses less energy and water per cycle.
A 40-gallon, fan-assisted draft water heater with an energy factor (EF) of 0.64 should serve you well.
For more information:
Read "What are the pros and cons of a tankless water heater? We are considering replacing our gas hot water tank." a Q&A answered by Danny Kelly.
Also, check Mick Dalrymple's answer to the question "How can I meet my hot water needs with a tankless water heater?"