Connecting them like you describe is called daisy chaining. It should work. But the recommended topology/ way to connect #2 and #3 to the main one/ #1, is to connect them directly to an unmanaged switch, where said switch is connected to #1 LAN port.
I wanted to follow up and see if you are still in need of any help. Please let me know if you are still having any concerns or questions from here, as I would be happy to take a closer look and assist you further.
Just one quick final check in here since activity has slowed down. We'll be locking the thread in the next 24 hours, but if you still need help, I would be happy to keep it open. If there's more we can do, just let me know.