Dualgender is a term used to describe someone with competing gender traits. Normally someone that is dualgendered has two different gender traits or "people" inside them that will sometimes conflict resulting in Dysphoria. Dualgendered people might identify as one of their gendered traits, and when their opposite gender conflicts with them they might switch to their other trait.
This is not associated with DID. This simply means that the two dualing genders are so vastly different from each other that they might feel like two separate people.