Thanks very much for the prompt reply about the current state of the setup.
I am not sure what could be behind the current inconsistent behavior you encountered, so I will need some additional details from your end.
First thing will be to check if there is a firewall active on any of the two machines. For testing purposes you can check what the remote execution behavior will be, if you disable the firewall. Or, directly include in- and out-bound rules for the following ports:
Scheduling Service: 8009
Storage Service: 8492
Execution Machine(s): 55555
If this still doesn't allow the remote execution, or is not applicable, please, clear the log files on the two machines, trigger a remote run on the second machine and give it some time. In a few minutes, you can collect the application logs of both machines and send them zipped for further inspection. The logs of both machines can be accessed through the execution machine details - double click a machine listed in the Execution status view, or open the Test Runner on the particular machine and use the logging buttons.
As a side note I would like to mention something in regards the message you noticed in the log of the remote machine - this is a standard message that a Firefox installation is detected and it is actually not related to the remote run. However, the logging may include any other details that will help me understand what the issue could be.
I am looking forward to hearing back from you.