The following image describes the problem:

Processor 1 has no RS232 channel, but has an SPI one, so we used a UART driver and a level translator ICs.
The two processors are on separate boards, and the RS232 receiver will be connected to them by one cable that will be split into two to be connected to each board.
How can we solve this bus contention problem?
Edit #1
Unfortunately, I can't modify hardware. Is there any software solution?
Edit #2
I thought of a solution but don't know if it's applicable or not. I read through the MAX3223 level translator chip datasheet, and found that if the input level to the IC is undefined "Irrelevant", the output is high impedance. I found the following function table in its datasheet:

In my circuit, FORCEON and EN~ signals are tied low and FORCEOFF~ is tied high.
How can I send an unidentified level to it?