Cut2D and VCarve share the same file format (CRV) so whichever one is installed last will become the default program for opening those files. All it means is that if you want to load a Cut2D file while you have the trial of VCarve installed you would need to go into Cut2D and load the file from there rather than double clicking on it in Windows. You could also right click on the file and choose Open With from the context menu.
If you upgrade to VCarve then your version of Cut2D would no longer be legal to use as the license is transferred to VCarve so you would delete it which will solve the problem as well. There's no need to have both installed as VCarve does everything Cut2D does and VCarve files are compatible with Cut2D (any VCarve only features are ignored by Cut2D).
The license for VCarve is the same as Cut2D. You can install on upto three computers provided you are the only user. So, for example, a desktop PC in the office/home, a PC/laptop in the workshop and a laptop for travelling.