My suggestion is to contact an experienced adoption attorney to advise you about the process in your State. I practice in Florida so the rules are probably different. Having said that when you say the other parent has consented, is this the non-custodial parent or your spouse? It sounds like the non-custodial parent. In California there may be specific prohibitions against this type of adoption if the person has a criminal record. Again an attorney in your area should be your first contact.
This information is provided as a public service to provide a general answer and should not be relied upon as legal advice.
Who denied your adoption? A judge or the local agency that did your home study?
What is important is to show the judge how you have changed over the last 12 years. Changes in circumstances - your maturity and stability. You should also have character witnesses who can vouch to your character. To present your case, you should have an adoption attorney present your case. You have an 11 year old track record with the child. You need someone to advocate for you and present all the positive things you have done for the child during the last 11 years.
I have seen this issue in Georgia. The court evaluator did not approve of the adoption, because the child's grandfather (was going to adopt her) had a criminal record with jail time more than 20 years ago. The judge looked at the big picture and granted the adoption. As long as your criminal history is not about domestic violence, child abuse or the like, you are probably alright. However, I would not try to present your own case.