+ AA6YQ comment sbelow
sounds like you do not have the K3 menu option CONFIG:PTT-KEY set correctly for RTS keying via RS-232/USB. You said you have Commander set to key the rig using the CAT port RTS line. You probably need to select CONFIG:RTS-DTR to match your Commander configuration, or the default OFF-OFF and let Commander use CAT commands for PTT by unchecking "Suppress CAT".
It also seems you so not have multiple PTT sources, unless something like DATA-VOX is also enabled, so the initial diagnosis may be wrong.
+ There are two ways to switch an Elecraft K3 between RX and TX:
1. by sending it the appropriate CAT command
2. by directing an external interface to assert or de-assert the PTT signal on the K3's backpanel
+ As Bill G4WJS has pointed out, a longstanding defect in the K3 can cause it to lock up if both of the above techniques are applied simultaneously.
+ I suggest that you first configure Commander to reliably switch your K3 between RX and TX using CAT commands.
1. To avoid the lockup defect, disconnect the external interface that is generating the backpanel PTT signal.
2. Uncheck the "Suppress CAT" box in the PTT panel on the Configuration window's General tab
3. Lower your K3's RF ouput power to 0, and tune to a clear amateur frequency
4. Using the TX and RX buttons in the PTT panel on the Configuration window's General tab, repeatedly switch between RX and TX. Does the K3 obey these commands without locking up?