How to reduce noise from the neighbor’s pool pump 12’ to 15’ away from the house

There are many different solutions depending on how much you'd want to spend, how much DIY you want to do, and what exactly you are trying to achieve. I would not try to directly switch this load: inductive loads generate voltage spikes when switching them, which can damage electronics and such that are not designed to handle it. They also have high in-rush startup currents which are beyond the normal ratings.

On the cheapest, very DIY side, I would use a definite purpose contactor for each pump (~$20, give or take), and run some smaller (14/2) wires inside to a switch.

The benefit here is the wiring going inside is low-current, and so you can use a regular lightswitch, count-down timer or programmable timer.

Insteon is another way to go. Insteon is a power-line carrier signal, which means it runs over your existing wiring. They have a high-current relay module which would be used to control your pumps.

You can then control from any Insteon-capable controller: there are a number of keypads, light switches, timers, home automation controllers, key chain remotes, motion sensors, and PC interfaces. The benefit of this is your "remote" can be anywhere (and you can even have multiple remotes). For example, here is a 6-button keypad that would work:

You could have a timer/controller set up to run your pump at certain times of day, or have a motion sensor that runs it if someone is in the pool area, or a button to manually trigger it. With a controller you can do very complex things, like have it run if someone is in the pool area for more than 30 minutes, or if it's manually triggered, and also ensure that regardless of that, it runs for at least 4 hours every day. Heck you can go crazy fancy and have it run more after it rains, or after it's particularly windy (to get leaves out).

I've linked to smarthome.com (who is the manufacturer of Insteon) but you can also buy their stuff from many other places, including Amazon.com.

There are equivalents to Insteon in other technologies (both wireless and power-line carrier) such as Z-Wave, UPB and X10 (though X10 is very poor technology, I would recommend staying with something newer).

You can also combine. For example, there is a UPB dry-contact output which you could wire up to a definite purpose contactor.

Most refrigerator alcoves are mini reverberation chambers, having hard sides. You may be able to place acoustic foam behind the refrigerator to absorb the sounds.

If you're handy sewing, you could copy this design for a sound reduction blanket using polyester fiber fill used for coats. As a trial, just loop a couple of layers of the batting off a couple eye hooks and leave space for air circulation. You may have to use some twine to belt it down flat. If it works, enclose in a cotton sack stitched down like a quilt.

To be clear, I'm only suggesting a flat wall hanging, nothing to trap heat.