A circuit diagram would help.
I assume that you are not sending data from the PIC16s to the PIC18
There is nothing wrong with sending serial data from one serial transmitter to several receivers. If there are problems, you need to see what is happening with an oscilloscope, or use a terminal emulator, such as a PICkit2 in UART mode, to see what is being sent.
If the presence of one of the PIC16s stops the other one receiving, then either the RX pin is sometimes outputting signals, or the levels or timing are marginal. You could try slowing down the data rate. You could also put a resistor, say 1k, in series with each of the RX inputs. That will stop them messing up the signal if they do become outputs at any point.