Figured out a pretty good system I'd say, using only mechanical stuff, no fluids involved. But you will need access to a very steady source of power (I suspect you have this because you have a mist generator). You will need two almost identical circuits of this pattern:
P
|
=IGO
=IGO
=IGO
=IGO
|
S
Where I, G, and O are all gear assemblies, each I is linked to one and only one of the inner plates, O's are similarly linked to the outer plates and G not linked to anything.
= is a horizontal which inputs exactly 10 net power into the system
| is a vertical axle
P is a power source that provides the exact amount of power consumed by all the G gears and vertical axles, but, IMPORTANTLY, NOT that consumed by the other gears, or by S.
S is a pump feeding water into the pool.
All the I and O gear assemblies are linked up to a lever and that lever is pulled, such that their default state is OFF.
Note that the system will be exactly 10 power short of activating the pump. When an inner plate is triggered, one of the I gears will switch to the ON state and introduce 10 power into the system, 5 of which is drained by the newly activated assembly for a net gain of 5. Conversely, each outer plate triggered turns on one of the superfluous O gear assemblies and drains 5 power from the system. Thus you need 2 more triggered inner plates than outer plates to activate the pump, and only under this condition can the pump input water into the pool.
Conversely, to remove water from the pool, you make the exact same circuit but flip the positions of the I and O gears, and have the pump pumping out of the pool.
Also note that the vertical axles are just a way of representing power transfer to and from S and P, the power can follow whatever (linear!) route you want, you just need to ensure that P provides exactly the amount of power that this route consumes.
EDIT: Also very important to note that you need a separate source of power for every input into the system, and it needs to be isolated from your main power source too. And you need to make absolutely sure that there is no linkage between the draining and filling circuits whatsoever.