Yes ARD will work over the internet. My current config has a mac at home that I can access remotely. I also manage my mom's mac remotely - she has DHCP ip from service provide, a quick script on her mac (auto running) updates Dynamic DNS free DNS freedns.afraid.org so I can just use "mom.homesystem.org" (example) and not worry about the IP address etc.
There are several guides that can be found via searching google etc.
Basically -
Set up the remote computer with a fixed IP address
Set up ARD
Open 5900 and 3283
Use a web page like http://www.whatsmyip.org/ to have your mom tell you her IP.
connect remotely
The guides I alude to above will detail all the bits needed and any config. ONCE its setup she won't have to change any settings on the router, nor report the IP address.