I went through the same situation ,except for me I didn't get a ticket, I had to go through courts to get a diversion for misdemeanor . Is the petitioner a Citizen or a GC holder. If a citizen , I doubt it will be any problem , make sure you have all the paper work, tickets fines and all that.

As far as undocumented work, its pardoned for a relative of a Citizen. You can read the who deal on the USCIS website.