So, is there any way to authorize a local user login remotely? Assuming the computer is connected to the Internet, is there any way to set up something that will ask for my authorization in order for the person to login when I'm not home? I want people to use my computer here at home, but i want to authorize it whenever they wish to use it.
This is relatively easy to do.
First off, you need to decide if you want users login on the built-in guest account, or you can create accounts specifically for them.
Once you make this decision, then the question is how you will remotely access the machine. There are a lot of options such as Remote Desktop, VPN, VNC, telnet, SSH, etc etc.
You can then enable and disable the account(s) as necessary via a GUI, script, or command line interface.
There are many ways to accomplish this with or without 3rd party tools. You just need to pick a method and go.
Edit: I reread your question. You are asking to be notified of authorization. That makes it a little trickier, but not impossible. My first thought would be to have the system email you on a failed log on attempt and include the username so you can enable it.