Quite possibly the importance of this law should not be overstated, and I agree with you and your children carrying on with your Coursera courses. But apparently you will be doing so in violation of the law.
Should not unjust laws be protested, if perhaps also disobeyed? I would not exactly be afraid to continue using Coursera in Minnesota, but experience has taught me that law enforcement should never be trusted 100% to be reasonable.
That said, you mentioned that you will be speaking with your state legislators -- you are doing as much to fight this as anyone reasonably could, and for that you have my gratitude. If 10,000 other Minnesotans took the same action as you, this would die as it deserves to.