This not a problem that has a technical solution. If there is a policy in place, and the user violates it (which is later discovered by normal, casual, non-forensic means), they are terminated. If a company really wants to get rid of someone they will find a way that generally does not result in them getting sued (which a policy that is worded like this may open them up to if they decide to enforce it), and there are much easier ways to terminate someone than trying to enforce and track remote laptop usage. The users being local admins, with unsupervised and exclusive physical access to the laptop just negates any technical controls you could put into place that would even make it worth your time trying to implement a technical solution to this.
Having a policy that says they can use it for personal use "except for..." is even more ridiculous. It is much easier for the policy to state that it can't be used for personal use period.
The trend in remote laptop usage is more focused around protecting the data on the laptop from falling into the wrong hands in the event it is lost or stolen which involves hard disk encryption usually.
One method that may or may not work for your org is to have no actual data or applications stored on the laptop, but have the user only use it as a VPN client to remote back to the office into a VM or terminal server to do all of their work. Their activity is much more easily tracked when all of their activity is going through the office, and if they don't login or have much activity after they do, then they probably aren't working (kind of an inverse to the policy your company is looking at). Also, if the laptop is lost or stolen, there is minimal impact to the company since there was no data on it to begin with. This of course, depends on what kind of work they are doing and if their job requires working with no internet access.