What you want to do is called "expungement". You want to expunge a guilty plea in a misdemeanor domestic violence case. The rules about expungement depend on the nature of the crime. Misdemeanors are relatively easy; domestic violence is relatively difficult. You should consult with a criminal defense attorney, who would pull your complete court file, review it, then tell you your options.
Provided you have not previously vacated a conviction, you may seek to vacate this conviction. However, a certain number of years must pass. For domestic violence convictions, the statute requires that 5 years have elapsed since completion of the terms of sentence. So, yes, there is hope for you, but it's a few years down the road.