Nobody's going to call the cops over a neighborly invite. What would the charge be? Menacing kindness? LOL. If the mom was overly irrational like you purport and starts freaking out, you simply say sorry, I wont bring it up again, and leave. If she calls the cops she will show herself to be irrational to them.
You scared she'll lie to the cops? Do it in front of the kids so they can witness.
This really is the age of the ninny, like Cooper said.
"Always place your clothes and weapons where you can find them in the dark"
"Understand that the enemy is not the enemy in his own eyes ;this may offer you an opportunity to make him your friend. If not, you can kill him without hate, and quickly."