My wife asked me for a separation as an attempt to save our marriage and then filed for divorce two months later? Should I move back in to our house?

The answer to your question is yes, you do have a right to move back into the marital home, unless your wife has secured some type of a court order that requires you to vacate and remain vacated from the residence. The answer to your second question on whether you should move back is a personal one. Again, unless your wife has some type of a court order that prohibits you legally from moving back, it is your home too. My only concern would be putting yourself into a situation where you are  not wanted, and whether if you do move back in, your wife makes up some phony allegations against you that you threatened her or were physical with her, to have you removed from the home. Ordinarily, we advise  not to move out of the home in the first place, until the divorce or separation case is filed, there is a first hearing scheduled before the court commissioner and your custody and placement rights can be determined by the court. I can only surmise from your post that you are a nice guy and moved out to give your wife some space as you didn't want a divorce, and once you moved out, used it against you to go ahead and file for divorce anyhow.

You can move back unless she has a court order that keeps you out; if you move back, be careful she doesn't set you up to allege that you assaulted her, in an attempt to get you out.