You have several issues going on here. The first is is that going 31 MPH over the posted limit is now a Class B Misdemeanor in Illinois. The potential penalty for a class B Misdemeanor is up to 180 days in jail and a maximum fine of $1,500. The offense is categorized as a Class B misdemeanor, which means it is treated as seriously as criminal trespassing, possession of cannabis (2.5 to 10 grams), and various identity theft laws. In short, this is not something to try to wing on your own.
Added to this is the fact that your child is a very new driver. On my website www.ZippToCourt.com, I have an entire traffic page that might be helpful to you. You should at least read the Illinois Parent Teen Graduated Licensing Program PDF from the Illinois Secretary of State. I have this PDF of this on my site which you can access directly here: http://zipptocourt.com/uploads/IllinoisGraduatedParent-TeenDrivingGuide.pdf
First off, hire an attorney for your child. This is critical. Most attorneys, including myself will give you a free consultation. As this is a Class B misdemeanor, you are going to find some attorneys wanting some serious cash for a retainer. I think if you call me, you will find I am far more reasonable, and I will explain why if you call. In any event, your child needs an attorney.
Because of the charge, there is zero chance of avoiding Court. Your child has a court date, most likely at the Mundelein Court House (just look at the bottom of the ticket for the date and time). What your attorney will do is negotiate on your child's behalf to hopefully convince the village attorney or state's attorney who has the case (just look at the issuing department - Village of Vernon Hills, Lake County Sheriff, Illinois State Police etc.) to find out which agency issued your child the ticket) to amend the charge to a lesser charge.
You can expect a fine and court costs. Also, your child will absolutely have to take traffic school due to their being so young.
I have taken traffic tickets to trial, but unless there is an incredible story to be told, and especially as the ink is barely dry on your child's license, you are looking for a negotiated plea in this case. Also, as you will read in the Graduated Licensing Program, your child has enhanced responsibilities and stricter scrutiny due to their young age. With a child this age, a conviction, which is always a possibility in a trial situation is not in your child's best interest. Through negotiation, and if this is your child's first and hopefully only driving offense, it is possible for your child to obtain the sentence of supervision which is an alternative form of sentencing and does not count as a conviction. If you wish to read the Illinois Supervision statute, here is a direct link: http://www.ilga.gov/legislation/ilcs/fulltext.asp?DocName=073000050K5-6-3.1
I am sure you have questions, please feel free to contact me or another experienced traffic attorney for more information.
This answer is marginal legal advice and does not constitute an attorney-client relationship. Every client and case is unique. The best advice is to always consult with an attorney. Free legal resources at www.ZippToCourt.com