Hi,
it is quite unusual that the server of a cluster is at the same time a desktop machine. If you usually submit the job from your Windows machine to the queueing system, and as I guess that your Windows machine is not the head node of the cluster, why do you want to submit jobs from a remote machine to a remote machine in addition or as an alternative? OK, sorry, questions about 'why' are more out of curiosity and not helpful as answers...
If ssh to the same machine works, the Run(network) option should work too. What comes to my mind when thinking about possible problems is the fact that the local directory and the remote directory must not be the same. Please try to set as working directory on the remote machine a different path than the one of your project.
Did you enable 'Expert settings' in the remote systems dialog and set a check at 'no password'?
Will you ALWAYS be submitting jobs to the local queuing system and not use another remote machine or cluster from this TmoleX client on that machine? If yes, you could try to fool TmoleX. Replace the ssh and scp binaries that you will find in the local TmoleX installation by scripts which simply do nothing but execute the commands that are given as options. It will be a bit of a puzzle to find out how to do that exactly (e.g. Tmolex will be called 'ssh user@machine mkdir /home/user/TmoleXProject/job_SP_1', so your ssh script has to ignore the first option and execute the rest locally. Same for scp which has to be replaced by a simple 'cp' but ignores the machine and the user name.).
Regards,
Uwe