Car insurance for geo-bachelor and unaccompanied spouse

Dumb question. Googling didn't lay out any clear answer. Thought I'd consult the military braintrust for all my options before believing whatever the first rep at Geico or USAA says. I am geo-bacheloring on unaccompanied OCONUS but US orders. I'm stationed in OCONUS "State A." Two-year orders. My spouse will primarily be living in "State B," with her own car. Her car is co-owned by both of us on a title in State A. I have my own car also titled in State A.

How do we handle car insurance? Will an insurance company just let me register the policy for everyone in State A?

Or will they say, sorry you need two separate policies? I fear I need two policies for the two households with both of us as drivers because we would likely drive each other's vehicles while visiting.

My spouse will be living with family, so adding her to their policy might be an option. But I'd like to skate by on the lowest cost option.