How can I remedy a multiple AirPort network where each base station tends to end up isolated from the rest? I live in a wide house, so I have an Airport extreme, an Airport express and a TimeCapsule setting up a free roaming network.
I used to have the Airport Express working as a master central router for the rest of the network.
Airplay was a little buggy and wifi gaming is not the best option out in the market.

But now I changed my ISP, and it provided me (free of charge) with a ZTE ZXDSL 9311WII routed modem, with 4 ethernet ports, so I decided to boost the performance of my network. Bought over 300ft of LAN cable, a bunch of cable connectors, crimping tools and even wall connectors...
So I wired every AirPort directly to the ZTE, and now I have all airports in bridge mode.

The problem that emerged is that a computer connected to one airport can not see anymore the computer in another airport. This happens if the computer is connected via wifi also, he can only see the ones connected to the same airport. Also, airport admin utility lost the capability of seeing all the airports connected and turned on - and now can only see only the one that the computer is directly connected to.

How do I solve this visibility issue?

I am SURE ZTE is not blocking connections because if I plug in computers directly to ZTE, they can see each other just as they should.
I already went trough all airport possible configurations, googled for the whole day, and found nothing about this configuration being possible or not.
The first thing I would suggest is to get an ethernet switch and place it between the ZTE router and the rest of the network.  Route all the Airport devices into the switch.  Then they should all see each other.  These cost $18-$25.  

I have two Airport Extreme Base Stations, at opposite ends of my house.  I set the one connected to a DSL modem to be the DHCP server, and create Airport wireless networks.  I select the channels manually, not automatic.  

The second base station is connected to the first by ethernet cable - not wirelessly.  It is set to bridge mode, but also to create wireless networks.  I give the networks the same, identical names, but manually select different channels than the first base station.  

This lets any WiFi device to connect to either server without any conflicts that I have noticed.  

You may wish to turn off the DHCP server on the ZTE router and use one of the Airport base stations to provide that service for your network.