Q: Apple remote desktop client

It is available for download from the App Store

It is not clear what you are referring to.

OS X has built-in a remote control function that often might be generically referred to as a 'Apple remote desktop client' for controlling another Mac but is more accurately referred to as 'Screensharing'. This as mentioned is built-in and does not need downloading and installing. See OS X Yosemite: Share your screen

The second possibility is that you are referring to 'Apple Remote Desktop' which is an administration tool for administering and remotely controlling multiple Macs on a network. See http://www.apple.com/remotedesktop/ and https://itunes.apple.com/gb/app/apple-remote-desktop/id409907375?mt=12

The final possibility is that you are referring to Microsoft Remote Desktop which is to allow a Mac to remote control a Windows computer or a Windows session on a Windows Terminal Server. See - https://itunes.apple.com/gb/app/microsoft-remote-desktop/id715768417?mt=12

Note: Microsoft Remote Desktop Client cannot normally control a Mac.

El Capitan will have the latest client built-in. However Screensharing and Apple Remote Desktop are not designed themselves to work well across the Internet, the issue being down to not having fixed IP addresses and Network Address Translation.

There is however a feature included in OS X that may make your life easier. The Messages application has the ability to not only 'chat' to someone across the Internet and to 'find' them for you based on their mobile phone number, email address, or AppleID, but can also initiate a remote screensharing request across the Internet as well.

See this article on how to do this - Messages (Yosemite): Share your screen

If Messages does not work, consider TeamViewer.com which works very well across the internet.

Paul Cohen1 wrote:

 

Looks good, but costs $809.00. Ouch!

It's free (for personal use). Read the ad again.