The problem that you are having stems from the The Real ID Act
. See Sec. 202 (d) (6) requirement that a State shall, "Refuse to issue a driver's license or identification card to a person
holding a driver's license issued by another State without confirmation
that the person is terminating or has terminated the driver's license."
Different states apply the requirement differently. Some will let you get an ID card or DL if all you have is an ID card in another state and others will deny you either a DL or ID card.
I don't know that state law cannot be stricter than the Act, which provides minimum requirements.