While possible, it's not very practical.
In order to do something like this, you'll first have to have some sort daemon(service) running on your laptop that is listening for a sign(command) all the time. This might be a web server or something similar, that when it sees a particular request, it executes a command on the laptop.
There are two problems with this, the first is that you'll have to write this listener yourself. That's not a simple task, especially for someone who does not already know how they would go about it.
The second problem is that it dramatically reduces the security of your laptop, leaving it open for anyone to run commands on it. Even if it's just to open a browser. You'd need to build some authentication system into it to protect it and that makes an even more complicated programming job.
A similar question
was asked a few weeks ago.
Another way to do it might be to have a Vera scene set a flag in a file, or something, and then have a scheduled task on your laptop that polls Vera regularly and if it sees the file/flag then it pops the browser. It's definitely not a good method, but it's one way.
If you stated your end goal, someone here might be able to suggest a simpler way to do it.