I was never arrested nor fingerprinted. I am happily married now in a new relationship
and expecting our first baby. The DV is the only charge on my record. What are the odds
of getting approved for a green card with this charge on my record?
Yes, a DV conviction WILL factor into any "status" application whether or not you were ever arrested or fingerprinted. And you should seek the assistance of a qualifed immigration/criminal attorney to assist you in this matter.