Using Apple Remote Desktop to view External HD files
I can not advise regarding Apple Remote Desktop since I do no have access to this software and I do not wish to purchase said software.

However, Apple's Back to My Mac free software can provide remote access to your home computer files and screen sharing.


  Note: The instructions shown below were copied from this Apple website.


If you have an iCloud account, and you have several computers connected to the Internet, you can share the screen of one computer with other computers.

For example, if you have a Mac at home that’s connected to the Internet, you can share its screen with a Mac you use at work. You can control that Mac, move files and folders, open or close apps, and even restart it.

Set up Back to my Mac
Follow these steps for each computer whose screen you want to share.


Choose Apple menu > System Preferences, then click Sharing.
Select Screen Sharing or Remote Management.
Next to “Allow access for,” select “All users” or “Only these users.” If you permit only listed users to have access to the screen, click the Add button  and the Remove button  to edit the list.
Choose View > iCloud to open iCloud preferences.
If you aren’t already signed in to iCloud, enter the Apple ID you use with iCloud, then click Sign In.
In the list of iCloud features that appears on the right after you’re signed in, select Back to My Mac.


To stop sharing your screen using Back to My Mac, open iCloud preferences, then deselect Back to My Mac.

Connect to your remote Mac


To see your remote computers in the Finder sidebar, choose Finder > Preferences, click Sidebar, then select Back To My Mac in the Shared section.
Open a Finder window. If no shared computers appear in the Shared section of the sidebar, put the pointer on the word Shared and click Show.
Click the remote Mac, then click Share Screen.

If you don’t see the Mac you want, click All to see all the available computers, select the one whose screen you want to share, then click Share Screen. All computers that are signed in to iCloud using the same Apple ID as your computer and use Back to My Mac are shown at the top of the list.


Back to My Mac requires a router that supports NAT Port Mapping Protocol (NAT-PMP) or Universal Plug and Play (UPnP) to share services. Check the documentation that came with your router to make sure it supports NAT-PMP or UPnP.

Some Additional Notes


To access files on the remote Mac from the local Mac, the remote Mac must have file sharing must turn on. To turn on file Sharing, apply the following steps to the remote Mac.  


Choose Apple menu > System Preferences, then click Sharing.
Select File Sharing.

The external drives on the remote Mac are not automatically accessible from the local Mac. To make an external drive accessible from the local Mac, apply the following steps to the remote Mac.


From the Finder application, right click on the external drive icon.
Expand General to view the Shared Folder checkbox.
Make sure Shared Folder is checked off.

If a remote Mac computer, folder or drive does not appear in the local Mac's Finder application, try relaunching the Finder application by applying the steps shown below.


Press the ⌘+option+esc key combination to view the Force Quit Applications window.
Select Finder.
Click on the Relaunch button.

You do not have to be logged in on the remote Mac computer. You can also login while the Mac is logged into someone else's account.
The remove Mac computer can not be a sleep. You must disable sleep in the Energy Saver pane of the System Preferences application.
While Screen Sharing, the Finder application on the local Mac computer had access to drives on the remote Mac computer.
You can mount the drives of the remote machine without sharing the screen. This will require entering a user name and password.
If you mount the drives of the remote machine using someone else's user name and password, then select screen share, you will login to that person's account on the remote Mac.