Is there a way to change my assault conviction?

Even if the State does not allege that the assault involved a family member, they can later prove it up if you were subsequently charged (and enhance the case to a felony.) The "family" part of the charge is generally not even discussed in negotiations - either it involves a family member or it does not. If you did not hit the person, set the case for trial! You should not plead guilty to something that you did not do and risk a future felony charge.