That is really the solution the cheapest solution that I can recommend is to store huge amounts of water in large container, like cylinders or drums, which can be bought at groceries like carrefour or lulu.
No need to have coolers. take note that this might just be a waste of time and money, as the temeperature of the water inside the tank can be too much, and hence, a really cool temperature is required to decrease this temperature.
I believe two containers, will be enough for your kids and you. Add one more pail, and i think it will be more tahn enough for your family to take a bath in the morning.
Just dont forget to save the water in the containers, before sleeping time.
If you are also taking abath at night, save water in the morning, after you take a bath.
Just dont forget to save water, everytime, so you can have ample amount of water like for washing the dishes, and the like. Washing the dishes during this time is also horrible, the water coming from the faucet is very hard to endure.

BUY THE CONTAINERS NOW AT THE GROCERIES and no need to worry about hot water.