In all honesty I can't say that i've seen any software capable of this. However, if it was me i'd do something like the following...
If Windows:
- Set up a VPN between you and your dads PC with some mediocre level of encryption.
- Map a drive to your dads server from your server.
If Linux:
- Set up a SSH server on your dads server.
- Connect to it using the SSH client on your server
For both:
- Use a program such as 7-zip to compress the data. 7-Zip command line tools can read what files you want to compress from a text file (so basically make a big text file with all the file paths that need to be backed up and then pass it to 7-Zip. Also tell 7-Zip to only compress files that have the "Archive" attribute set.
- Get 7-Zip to unmark the "archived" attribute on each of the files once it has been zipped. The archive attribute will automatically be set again if the file is modified.
- Get a script/batch file to move the zip file to the remote server. if its windows, it will be a simple case of telling it to move it to another drive, if its linux you'll need to look up the SSH SCP commands.
That, in a nutshell should do it. Only files that have been modified since last backup will be zipped and all data will go over a secure connection.