The 2nd one connects to the 1st by Wifi.
Thanks for the clarification on that.
The reason is that all the ethernet [out] ports on the 1st are taken by other more essential devices
You do know that you can always connect an Ethernet switch to one of the Ethernet ports on the AirPort to create more Ethernet ports, correct? Switches come in 5-port, 8-port, 16-port, etc versions.
An example of an Ethernet switch would look something like this:
You would connect an Ethernet cable from one of the Ethernet ports on the AirPort to Port 1 on the switch. That will leave 7 available Ethernet ports on the switch for devices, plus you would still have 2 ports left on the AirPort. If you used a 5-port switch, you would wind up with 4 additional ports for devices at the switch.
You can also connect an Ethernet switch to another Ethernet switch. For example, I have an 8-port Ethernet switch connected to my "main" AirPort and another 8-port Ethernet switch on the other side of the house that connects back to Ethernet switch connected to the "main" AirPort. So, in effect, I have 7 Ethernet ports for each AirPort, not counting the other 2 free ports on the AirPorts.
It would be also difficult to hardwire the 1st to the 2nd/3rd because of building structural issues.
Understood. Sometimes, you just can't do things the optimal way.
Would the problem be solved by connecting the 2nd WiFi to the First through an ethernet hub?
Not sure what you mean by Ethernet "hub". Do you mean Ethernet "switch", like the example above?
If the 1st AirPort is connected to an Ethernet switch or hub and it gets its network Internet connection that way, and you could also connect the 2nd AirPort to the same switch/hub......then.....the 2nd AirPort would not need to use the much slower WiFi connection to connect to the 1st AirPort. You could also connect the 3rd AirPort to the 2nd AirPort or to the Ethernet switch using another Ethernet cable connection and maintain the much better Ethernet setup for the AirPorts.
Having all the AirPorts connect using Ethernet is far and away the best way to set things up if possible.