by default, the check_local_disk is defined as:
'check_local_disk' command definition
command_line $USER1$/check_disk -w $ARG1$ -c $ARG2$ -p $ARG3$
If you launch check_disk without any args, you'll see that the option -p stands for "path".
Meaning that you just have to put /home as the 3rd argument
=> check_command check_local_disk!50!60!/home