I remember your question before. What the lawyers in the forum concurred is that you should not have any problems since it does not make you a public charge to have received help in that isolated oportunity.
I agree that this is a very tough case and the chances of getting the waiver are little, but if they don't do the waiver the chances are reduced to zero. The worst thing they can do is doing nothing. Immigration officers have a lot o prosecutorial discretion and if a good humanitarian case is made they can grant the waiver. I also believe there's nothing impossible for God and He can move anybody's heart.
You should contact an immigration attorney to review the convictions to check whether it's for a crime involving moral turpitude or an aggravated felony. Since they are here illegaly, also it's important to evaluate if there's any immigration relief for which they qualify.
You should really have an experienced immigration lawyer review your criminal documents to evaluate the merits of your case. To naturalize you need to prove that you have been a person of good moral character for the last 5 years. You mentioned thay you had a DUI 6 months ago. That's detrimental to your showing of good moral character, especially if there were damages to property, or persons injured. Moreover, even if you were not found guilty on the other 3 cases, if anywhere in the record...
You may file a fiancee petition on her behalf, provided that you have seen her personally within the last two years. Or you can marry her and file an alien relative petition. Consult with an experienced immigration lawyer to explain to you how the process works.
Normally your husband wouldnt need to go to the interview, but it would be a good idea to bring evidence that you are still together, such as receipts, bank statements, etc. since you qualify for the naturalization as the spouse of a United States citizen.