@bluebellsinthewoods I am so sorry for your loss and understand your need to have some personal space - especially just now.
I think it is entirely reasonable to be setting ground rules around when she stays at yours. Particularly about her not staying in your house, when your son isn't there. That's really not on and is taking the piss, especially as, I assume, she isn't paying anything towards the extra cost she will be giving you?
I would have a quiet word with your son first and find out if there is something going on in this girl's home life which means she doesn't feel she can go home. Depending what he says, it might help you to decide exactly what ground rules you want to lay out. If she is definitely going to University in September and in a different town a long distance away you might just want to lay out the one ground rule that she isn't in your house, when he isn't there.
On the other hand, if there is no major problem with her going home, then yes, I would be laying out all the ground rules right now, such as how many nights per week she can stay, any nights she can't stay ( e.g. a Sunday night, as someone else said) and definitely, she doesn't stay in your home while he isn't there.
At the very least, you need to tell him what you have said here, that you need your own space, especially just now, and it really isn't on that she stays in your house when he isn't there.
I, personally, wouldn't be getting into a discussion with the GF - I would be discussing it only with your son - and getting him to tell her what the new ground rules are. At the end of the day, it is his responsibility to have the difficult conversation with her.