I dont think you are being a prude (or a dumbhead!) at all. They are both so young, and i think that staying at each others houses, let alone in the same bed is a massive step. I feel the same way you do, and I would prob go even further out on a limb and say no to sleepovers full stop at their age(now who's the prude!?)

I agree with the other posters, that its your house and your rules. And if she has any ounce of respect for you, then she will do as you wish.

Good luck hun, hope it all worls out for the best x