You can try sending
psql to the background:
psql -f your_sql_file.sql &
Or, connecting to the local DB, you can use
dblink to dispatch a query to the remote DB:
SELECT dblink_connect('your_connection_name', 'your_connection_string');
SELECT dblink_send_query('your_connection_name', 'your_query');
dblink_send_query can only send one query at a time. So, if you want to run multiple SQL statements, this is not your solution.
Or, you can start a
pg_agent job on the remote server, which requires no manual intervention, therefore the state of your home box has no effect on running your job. The same can be achieved by setting up a
cron (or even better,
at - thanks, Erwin) job executing your script.
Additionally, if you have a long running job which you start manually, you can start a
screen session on the server and run the file from there. In this case, you can log off and go home, and the script will keep running.