Hello, my question is this title, but let me clarify a little: I had the Sonar Artist and when I bought Sonar Premium, I kept them both, but I'm thinking of uninstalling the Artist to put it in the notebook.
My question is if I uninstall it, can I in any way, in any case, compromise Sonar Premium?

It may. I have not uninstalled a Cakewalk DAW in some time. All Cakewalk DAWs rely on programs installed in the "Shared Utilities" folder. Uninstalling may remove those programs. It is not that big an issue though, re-run the Platinum installer and everything will be put back.
 
I assume you paid an upgrade price for Platinum. If this is the case, you have one license to use SONAR. Still, there is no need to uninstall Artist in order to install it or Platinum on a second machine. You may install either version on a second machine as long as both are not in use at the same time. There is little difference in the resource requirements between the two versions so you might as well install Platinum on the notebook.

As scook said, I would leave it alone. I un installed X3 from my main DAW once and it caused a bit of a mess with Plat. I had to use System restore to put it all back, I guess I could have just run the Plat installer too. So myself I don't recommend uninstalling unless your needing more hard drive space. 
Just a few things I did was I deleted the desktop icons and also made sure Plat was the default app for CWP and MID files.. For a while Professional was opening when I started from a folder. It would take me a while to even notice I was in the wrong version. 
 
And as scook said, Sonars licence is very liberal. First, you don't need to de authorize to install on another computer. And you can have it on a few machines within reason, there is no set limit as far as I can tell. As long as your the only person using it you are legal. I have Plat on 3 computers. One I never use as a DAW and it's only there so I can check things out while helping on the forum. 

scook
 
I assume you paid an upgrade price for Platinum. If this is the case, you have one license to use SONAR. Still, there is no need to uninstall Artist in order to install it or Platinum on a second machine. You may install either version on a second machine as long as both are not in use at the same time. 

I am pretty sure you can do that without having to defend yourself in court, but the general understanding of an upgrade license is that it gives you a new license to the new product, but that it vitiates the license to the old product. Sometimes it is explicitly stated that you are required to uninstall the old version and even destroy the old version installation media. If that is Cakewalk's interpretation, then your Artist version is unlicensed, but your Platinum is eligible to be installed on more than one machine. 

Yes I upgraded from Professional and it is still 100% available to me in CCC.  It certainly didn't just disappear.  
It shows as orange because I have the option of throwing money at it to bring it up to date. It is mine to use and install on other computers, but like all versions it's for MY use only. So in a way it's obsolete and of no value to me anymore. But I own it forever stuck at Aug 1 2015.   
 
You will see by the latest e mail that as of May 1 the updating will change and as they are saying you will pay the difference in price and there will be no more "deals" So I think anyone who missed the lifetime upgrade has missed the boat and it does not look like that deal will ever return. Those of use who did score the deal got a heck a break.. But now I'm waiting for the other shoe to drop and what will be the next offer to pry money from me somehow. 
 

What I would do, is uninstall Artist, then reinstall Platinum.