Wiki says that average tubs range between 40 and 70 gallons.
My showers usually don't last more than 3-4 minutes. If you can stand it, just live with the cold water during the summer months and use the hot water only when it's necessary. I learned some useful shower tricks while taking showers in Mexico at a place with no water heater and in December. (Yes. It gets cold there.)
I tried to just tough it out initially, but that left me almost purple when I got out. So what I did, when the water was too cold to stand, is slip your body in just enough to wet yourself. You only need a light sheen to build up a good lather. While you are soaping up, don't even stand near the water. Move to the back of the tub. To finish up, hustle under that ice spitter and wash off as quickly as possible. I survived like this for 2 weeks and didn't once get hypothermic.
If you don't use the A/C anyway, a nice cold shower in the afternoon should hit the spot and leave you feeling fresh for the rest of the evening.
As far as advice for actually solving the problem, I'm no electrician but if it's throwing the fuse on the washer/dryer, then there almost certainly has to be a short somewhere that is constantly drawing juice out when the swith is on. Get yourself a cheap voltmeter or a Kill-a-watt and test those main lines.