From the USCIS Website:
Who is eligible to receive deferred action under the Department’s new directive?
Pursuant to the Secretary’s June 15, 2012 memorandum, in order to be eligible for deferred action, individuals must:
Have come to the United States under the age of sixteen;
Have continuously resided in the United States for at least five years preceding the date of this memorandum and are present in the United States on the date of this memorandum;
Currently be in school,...
Most likely your matter was denied due to abandonment. Because it was a consular interview, they probably did not initiate Removal Proceedings. In my opinion, you would qualify for the new policy change. You must have an approved I-130 to begin. You may also file anew if you cannot lay your hands on the previously approved I-130. Best of luck!
I would suggest that you also speak with the lawyer about filing a "Padilla" Motion to Vacate his 2002 conviction. While the conviction stands, I'm afraid your husband is in a very dangerous predicament.
First and foremost, contest the citation and go to court. I have found that even if you have no defense, there are many opportunities to resolve the issue. You'd be surprised at how often cases bet dismissed at the clerk's level. Second, try to correct any problems you have with the vehicle prior to the hearing and be prepared to show the documents to the court and display humility. Be very careful about he time restraints on contesting a ticket. Often they are as little as four days....
Your infidelity is not a per-se bar to Citizenship and should not cause you a problem. They may though inquire as to the bona fide nature of your marriage if the issue comes up. If you are able to demonstrate that although you had an affair, your marriage was not for the purpose of obtaining lawful permanent residence you should be alright. All the best!