How can I keep my computers cool in a 100 degree house?
You need an ultimate-heat-sink OUTSIDE the house

Here's what you can't do: Server makes heat in box, A/C moves the heat out of the box and into the tiny-house, tiny house copes with ambient + solar load + server load + A/C load all stacking to make it so hot you can bake cookies.  At that point, the A/C, will break down due to not being able to transfer the heat from the Freon to the too-hot environment.

So every solution must remove all server and A/C heat entirely out of the building -- and if it removes solar load as well to make the place habitable, that is fine.  

Put the box on an outside wall

In this case, you mount the air conditioner on an outside wall, and enclose the A/C cool side with the servers.  This will have a big problem: accessing the A/C controls.  A wired remote will cure that; a remote thermostat won't since the thermostat will be in the wrong place. A wireless thermostat may have trouble with UV line-of-sight. In this case the A/C unit needs 3.4 BTUs per watt consumed by the servers, just to break even, and that assumes ideal conditions.  So you would be wise to upsize the A/C unit somewhat.

A carefully oversized unit would allow you to open the house-side door to the server box, and let the unit cool the entire house.  

Downside: It will be L-O-U-D all the time.  It will be like sleeping with a running vacuum cleaner.  Your neighbors won't like it either.  

Big downside: When the A/C cycles off, you have a problem. It must wait awhile before restarting, due to a problem called "short cycling".  Meanwhile the box will very quickly heat up, and as it heats up, cooling fans/heatsinks becomes even less efficient, creating a vicious cycle.  The box could critically overheat before the A/C is ready to run again.  The way you solve this is  by having a much larger "thermal mass" to share the heat with. But water jugs won't cut it because they have too little surface area to interchange heat quickly.  You need something with a lot of surface area, like... the rest of the house.

Air condition the whole tiny-house 24x7

In this case you don't bother with a box, just mount the servers where convenient and mount the air conditioner(s) where convenient.  As far as air conditioner size, you will need the normal BTUs + 3.4 BTUs per watt of power actually consumed by the servers. So if you have 3000 watts of servers you'll need 10,200 BTUs additional, on top of the normal BTUs your tiny house will require.  That math works because servers convert 100% of their power to heat. 

Downside: you are paying to cool the entire house all the time, even when you are not there. 

Water cooling on the servers

In this case, you fit water heatsinks onto the major heat-making components, and plumb them so you can carry the hot water outside. 

Skip through what these guys did.  They did a lot of mistakes and wheel-spinning that totally defeated the effectiveness of the project, because they are dumb and it was a stunt for a video.  But the principle is good. 

I'm not a fan of how they use copper instead of cheaper stuff like PVC (humans won't drink it; no need for PEX).  In fact, the long uninsulated copper pipe runs acted as a radiator and dumped all the heat right back into the room,  completely defeating their project.  They also failed to design "high spots" for bleeding bubbles. All easily fixed.  Also, keep in mind these guys promote products for a living, so for instance they did a very stupid radiator design simply to use that manufacturer's units, which were totally unfit for the application.

A sensible person would go to a pick-your-part type junkyard, and obtain a radiator assembly off an SUV. Including radiator, shrouds, fans, thermal switches, fan relay(s) and wiring harness bits.  Wire it so when the thermoswitch closes, it starts up the fan(s), which you power from an adequate 12V power supply.  All this stuff is designed to live outside, obviously.   

An SUV radiator is so large that I doubt the fans would ever need to run if it's not in direct sun.  That means the cooling system runs near silent.  The only thing running is a water pump. 

Also, you would never use plain water, not least because stuff grows in it.  Use propylene glycol antifreeze (won't kill cats and dogs), or mineral oil. 

Downside: This only cools components with cooling plates on them.  The rest of the components will still be adding heat to the box, and that too must be removed.  You could help that with another radiator inside the box, and putting it "first in line" for cooling: so the cooling flow is external radiator  -- in-box radiator -- CPUs -- VPUs -- external radiator.  Water cooling is so darned efficient that it won't matter if the water arrives at the CPU somewhat hotter.