Multiplexing UART TX/RX line
Your solution is correct, but your enable pin will be inverse-logic (low for enable), which isn't obvious in the schematic.

In general, the way to solve this sort of thing is to write out a truth table for the desired system. In this case, treat each slave TX in isolation. You want the slave's TX line to be high whenever the slave enable line is high (to make it an inverse enable line, put a "!" in the name, so "!TXn_EN." EAGLE will put a bar over the name), and you want it to follow the TX line whenever the enable line is low.

I don't know how to make a table in this editor, but if you make one up with that description, you'll find that it's a simple OR gate.