Your mom is right about the fish tank. If you change all of the water at once it will shock the fishes system cause it will be too sudden a change in water temperature as well as chemistry (pH, alkalinity, etc).
Turtles are tougher and not quite as sensitive as fish are, but you should make sure to use roughly the same temperature water to put back into the tank. Also are you carrying the tank with water in it??

I hope not. You don't have to scrub out the entire tank each time you do a water change. The algae and bacterial slime that grows on all the surfaces is not bad for the turtles. In fact they are beneficial in keeping the water cleaner by feeding on the waste that the turtles expel.
When I clean my turtle's tank I just use a siphon hose to vacuum all the dirt that settles on the bottom of the tank. I usually siphon out about 25% of the tank water and replace it with fresh room temperature water. The big thing is cleaning the filters. You want to rinse out the solid waste but you don't want to scrub everything bare since the bacteria that live in the filter are the beneficial kind. Also don't replace all of the filter components at the same time. Alternate which parts get changed, again so you don't wipe out the biological filtration.