My girlfriend wants some space right now?

I hope not, for her sake. You seem to have umed extraordinarily quickly on very little evidence that she was up to no good behind your back, and your tactics for getting at the truth sound better suited to a police interrogation. If that's how you responded every time she was out of your sight, it's frankly no wonder she wanted space. And if you did have reason to distrust her, then it was inbent on you to decide that things weren't working and leave it at that, not browbeat her into a confession. If I were you, I'd take her up on the original plan and give yourselves some distance for a while.