99% of the time mediation is the best route. You are in that other 1%.
You should immediately find a good lawyer, give them a written list of your absolutes (asset %, support amount, support duration, custody split, future child/education expense slit), pay the retainer and completely remove yourself from the process.
In some cases you may have to attempt mediation. If you do, go with your lawyer and agree to nothing unless they tell you to.
As for the grocery bills, she is probably getting cash back and buying gift cards. That is SOP for people in her situation. I bet you wouldnt believe how much cash and assets she has that you dont know about.
