I don't want to sound condescending or mean, please apologies if I do, but either get an attorney or a preparer to file for you, or spend some significant time here in VJ to educate you and your wife about how the process works and what to expect.
There is absolutely no way your green card will be here by the time you plan on travelling. What you will get is a 48- month extension letter, which she will need in order to get back to the US, and to prove status in general. For the trip, she should take her passport, her expired green card, the extension letter and your marriage certificate if she has changed her name to yours.
You should really just use your new address from now on. As others have stated, USCIS can do surprise visits, if they go your parents' house none of you are living there. Better to keep everything streamlined. Also, sign up for USPS informed delivery with your new address so that you can know what you're getting in your mail daily.
Please read the Removing conditions on this website WITH YOUR WIFE today. Make sure you both understand the process. Do come back with questions.