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.