You likely will need a lawyer to review the documents to see exactly what the court restricted and on what basis. If you need permission to move out of state with your children from the court, you would need to start a separate proceeding by motion.
A mediator will not represent either one of you, only try to help you both reach an agreement. A mediator will not advocate for your or your spouse's interests. A mediator will not appear in court for either of you.
With all of that property on the line, and issues of spousal maintenance looming I strongly suggest you hire an attorney to help you in a divorce matter.
Obviously you have rights to the property, as you're saying. However, yes you can turn over that right to them. Consult an estate planning and/or real estate attorney to determine how to do this as there may be tax implications and he or she will have to work with your spouse's estate.
This is an estate planning question. Your son should get a will. This will allow him to specify who the executor will be (assuming they accept the appointment) and who will get his money. There will be no guesswork or uncertainty. A Minnesota estate planning attorney can help him draft a will to meet his needs very easily.
She may be able to come after the value of them (not your sale price) if they're determined marital and you get rid of them in anticipation of a divorce. A judge can basically get the 1/2 marital value of that property from you in other ways. This is assuming it is marital property, which it may not be depending on the facts of your situation.
In addition, any judge will see through what you're doing quite easily and be unimpressed by such an unethical move on your part if and when it...
Outside of the legal process, I'd identify what the barrier is to your ex completing this task and try to work around it. You've said that he agrees to the adoption so it shouldn't be something you'd need to go to court over.
And no, contempt would not be a course of action unless there is a court order in place ordering your ex to enter the originals.