A lot of designs just use quad analog switch IC's like 4066, 14066, 74HC4066 etc. They have 4 independant switches that will allow data either way, and are fairly tolerant of spikes etc. They are common in digital port switching and are also used in VCR DVD equipment to switch AV signals to all the AV ports. 2 chips gives you 8 switches, so will switch 4 devices RX+TX.
But if your 3 target devices are not all connected at once, you can just parallel the RX and TX pins to all.