You need to configure the other two as just access points, not routers. Then connect the three together on the wired network side. The wireless and wired networks that connect them to the trendnet near the proxy, need to be layer 2 bridged together. Then confirm that you can connect to each one on the wireless side, and that you can then connect to the proxy.
You are correct that they need the same SSID, and also be on different channels. Use only channels 1, 6 and 11 and fix these. Do not use the automatic channel feature, these rarely work, and if they see some interfernce they change channel, and disconnect all the users. The channels 1, 6 and 11 are the only non-overlapping channels, so they don’t interfere with each other.