It is now possible to stabilize and move the laser with both stages.

The software and hardware settings are attached.
For synchronizing with the laser pulse we use following frequency generator settings:
period: 200us
high: 5V
low: 0V
duty: 50% 

The frequency generator is triggered with the external Q-switch trigger signal, that is in coincidence with the ESR HF.
To use the stabilization one has to use the external and NOT the q-switch mode of the laser.