Try:
bash -c '[ -d my_mystery_dirname ] && run_this_command'
This will work if you can run bash on the remote machine....
In bash, [ -d something ]
checks if there is directory called 'something', returning a success code if it exists and is a directory. Chaining commands with && runs the second command only if the first one succeeded. So [ -d somedir ] && command
runs the command only if the directory exists.