You have to first determine your DV conviction meet the standard for deportation first.
If Yes, then you are in trouble, if not, you can renew GC and apply for citizenship as long as you are out of teh 5 year statutory period.
According too law below, if DV is deportable, then it does not matter it is misdemeanor or felony because
criteria for deportation does not specify maximimal punishment.
http://www.uscis.gov/ilink/docView/SLB/HTML/SLB/0-0-0-1/0-0-0-29/0-0-0-5667.html
(E) 6/ Crimes of Domestic violence, stalking, or violation of protection order, crimes against children and.-
(i) Domestic violence, stalking, and child abuse.-Any alien who at any time after admission is convicted of a crime of domestic violence, a crime of stalking, or a crime of child abuse, child neglect, or child abandonment is deportable. For purposes of this clause, the term "crime of domestic violence" means any crime of violence (as defined in section 16 of title 18, United States Code) against a person committed by a current or former spouse of the person, by an individual with whom the person shares a child in common, by an individual who is cohabiting with or has cohabited with the person as a spouse, by an individual similarly situated to a spouse of the person under the domestic or family violence laws of the jurisdiction where the offense occurs, or by any other individual against a person who is protected from that individual's acts under the domestic or family violence laws of the United States or any State, Indian tribal government, or unit of local government.
(ii) Violators of protection orders.-Any alien who at any time after entry is enjoined under a protection order issued by a court and whom the court determines has engaged in conduct that violates the portion of a protection order that involves protection against credible threats of violence, repeated harassment, or bodily injury to the person or persons for whom the protection order was issued is deportable. For purposes of this clause, the term "protection order" means any injunction issued fo r the purpose of preventing violent or threatening acts of domestic violence, including temporary or final orders issued by civil or criminal courts (other than support or child custody orders or provisions) whether obtained by filing an independent action or as a pendente lite order in another proceeding.
