Can I still get shared custody if I am stable and always involved father with a history of alcohol use?

I am a stable father who has always been involved in all aspects of my children's development including feeding, bathing, nurturing and bonding. I have a full-time job and a good home for my two young children. I have a history of alcohol abuse that includes a DUI 3 years ago. My children have never been affected by the few relapses I have had since then and have never seen me drunk. My wife and I recently separated. I filed for custody protection and am seeking joint legal and physical custody of our children because they need equal access to both parents and have never been without me. My wife is trying to claim that she is worried about having the children sleep at my house and wants sole physical custody due to my alcohol use although never had an issue with me when we were together. I have been sober for 8 months and I receive regular injections of Vivitrol to assist in maintaining sobriety as well as regular visits with a therapist.