BerlinerAngelino

A criminal conviction is not the end of the world - it just depends what it is.
You will have to provide details of the conviction (showing the offence code) and sentence. Put as much as you can up front - you will probably get RFE'd for the rest, or just send it in as soon as you have it.
You will have to do it again with the N-400 at a later date.
 
Without delving into the details of Nevada penal code, as it is a misdemanour and not a felony (or worse, an aggravated felony) you *should* be ok.
However, pleading no-contest was imho not a wise thing to do, especially with another party (ie, you) who is not in any way a co-operating witness, and is claiming there was no issue in the first place.
If pleading no-contest was on legal advice, it was poor legal advice, but it is what it is. Unless you can somehow backtrack on that plea, have them re-open the case and plead not guilty, it isn't going anywhere and you have to deal with the consequences.
Just be honest, that is all you can do.
 

My friend had a similar situation but she was the victim and her husband , US Citizen, was the perpetrator. There was still an open case against him. They went to the interview with their four children. Th officer first talked to their lawyer and without even initiating an interview, they were told to go home. They didn’t know what their status was and the lawyer said she needs find a way to drop the charges. She tried but it couldn’t be reversed. While waiting months, she finally got a her 10 year green card in the mail. Having children together is big proof that your marriage is bona fide. My other friend, he was awaiting Naturalization and with a criminal record of theft and he is now a US Citizen. I really advise you to hire a lawyer since your situation is complex.

If you haven't already, you should also go alone to separate anger management counseling (not online), which shows both your support and further acknowledgement of your role in the incident. Also add for the two of you together some in-person marriage counseling. You could thus have two people, your personal therapist and the marital therapist (should never be the same person!) in your corner.
 
Take the money you're saving for a house and secure the services of a good immigration attorney now, to be on retainer in case a sudden problem arises. Wouldn't even think about getting pregnant until this is all over.