The kinematic is basically how your 'joints' are mapped to your machine 'axis'. In your case of a lathe you have one 'joint' (ie motor) set up so the x axis moves towards the operator in the positive direction and the other 'joint' (ie motor) moves the Z axis perpendicular away from the spindle in the positive direction. As you have noted above, to reduce the stock diameter with the front tool the cross slide needs to move away from the operator in the negative direction. If you want to use the back tool the cross slide will need to move towards the operator.
One way to achieve thes would be, as has been mentioned, to change the sign of the x coordinates in the Gcode when the back tool is to be used. This of course requires the gcode to be processed accordingly.
Another possibility is to 'switch' the x axis' direction when using the back toolpost. This can be done using a user defined M-code ( in the simulation configurations that come with version 2.9pre M428, M429 are used for example).
So the configuration would start in, say, M428 (ie regular front tool mode so all Gcode commanding x in the negative direction moves the cross slide away from the operator into the stock) To use the back tool post you would call M429 to change the x axis direction and now all Gcode commanding x in the negative direction moves the cross slide _towards_ the operator also into the stock.
If you wanted to get fancy you might even be able to remap the M6 toolchange command to call M428/M429 automatically according to wich tool number is called.
There are a few things to watch out for with this approach though. For example you would not want to rehome the machine while in M429. Also moves in machine coordinates would need to be avoided and coordinate offsets would need to be handled wisely. Although that probably is true for all lathes with front and back tooling.
The other thing is the tool compensation which I'm not really familiar with on lathe setups, so that would also need to be tested carefully.
Note that this feature is only available in version 2.9pre 'master'.
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Usually I try to provide a simulation configuration to demonstrate switchable kinematics but I have only limited time at the moment to create a vismach model of a lathe. I'll see what I can do.
