Do we still have to stay in our house together even if I already filed a divorce?

I am not certain I understand your question. In Arizona if you were to move out of the house pending the dissolution that would not be seen by the court as you "abandoning" the house. One of you could ask the court for exclusive use of the house, but remember that if you are awarded exclusive use you would probably ordered to maintain the mortgage payments. It is important that you speak with an experienced family law attorney in your area to explore your options.

You no longer have to co-habitate upon filing for divorce or seeking legal separation, even before they have been actually granted.

No, you can live anywhere in the county. You cannot leave the area or Florida with the children without court approval or consent of the other parent.

Nothing requires either of you to stay in the house. That being said, it would be prudent to make a motion for temporary orders immediately after filing the petition for dissolution to determine who gets to live in the house pending the allocation of assets.