Husband's house in VA, mine in TX - how not to pay VA state taxes?

My husband owns a house in VA and I recently bought a house in TX. I work remotely and plan to update my address with my employer to TX, which will entail a pay cut.  We plan to be back and forth between TX and VA. My car registration and driver's license are still VA and my bills go there though I can update those items to TX.  Is there any way I can avoid paying VA state taxes if we split our time and if my husband maintains his home?  If not, would it help if my husband updated his information too (but kept his house)?