There are a few questions related to this topic already:
The answers to these questions might help you, though I'm not sure if any fit your needs exactly.
It's not clear from your question, but when you say "our computers are not tied together in any way", are you implying that you want some way to get the software onto your relative's computer without having direct access to the laptop? If so, be forewarned that a) that is very difficult, b) is almost certainly illegal in most jurisdictions, and c) is not something which we will help you with on Super User.
Regardless of how you are attempting to do this, please make sure you consider the legal and and ethical ramifications of spying on somebody, regardless of your intentions. Even if you have access to the computer, there very well may still be laws prohibiting the installation of tracking software without their permission.