Wifi to other building

[AddeBjerndal]

Hi, I have some issues with getting good connection to another building on my property (my garage). 
I have 3x Nest Wifi Pro, where #1 is connected to the modem in the main building. #2 is standing by the window closest to the garage, and #3 is in the garage by the window facing the main building (about 15m away). 
I only get weak connection on #3, and I'm installing a charger that needs wifi. 

I've read that the best way is to hardwire the APs, but that means I have to connect a ethernet cable to #1 and drill a hole through the wall so that the cable can go outside all the way to the garage. 

Is there a better way to do this? 

Can I for example connect I cable to #3, put it in the ground, make it go through the wall and hardwire to a socket on the inside? Elko RS infällt nätverksuttag Cat 6 | Clas Ohlson
And then connect my #1 to the socket? 
Or does the #1 have to be hardwired to the socket and then #3 is the one that I have to connect to the socket?

Ihttps://imgur.com/a/JSKJJNn

[MichaelP]

As long as those two sockets are connected to each other, or are both connected to an Ethernet switch that is not connected to the outer network, yeah, that should work.

[AddeBjerndal]

Yes the idea is that the socket in the maintenance building is connected to a socket in the other building via a cat6 cable. And the #1-Nest that is connected to my modem also connects to the socket via LAN. And the #3-Nest in the other building connects to the socket in that building. 

In that way it should be the same solution as if I connected #1 and #3 with a cat6 cable. Or am I totally wrong? 

[MichaelP]

Yeah, like I said – that should work as long as those jacks are wired the way you think they are. I would probably try to test that connection using something like a laptop first, just to be sure it's live and operating properly.