In your scenario, the package will run on your local PC.
You have a couple of options. RCmd or another utility will execute a command on a remote machine. This would mean you have to have a service running on the remote machine.
You can run the package through the SQL Job Agent. Starting a job will run the package on the server the Job Agent is running on. You cannot run the same job twice at the same time, so if you have a multi-user environment you would have to dynamically add a job to the agent to support this. It's not a bad option, but it can be tricky to set up security.
You could also create a stored procedure using CLR or xp_CmdShell to execute the package on the SQL Server that procedure runs on. This is again a place in which security can be tricky, but it gives you lots of flexibility.