This is how we deal with Domestic Discipline in public
My wife and I like to keep our lifestyle private apart from close friends who we can trust, so I have devised this way of letting my wife know what I am thinking without anybody else having a clue or looking at us strangely.
My Wife has to carry 2 packets of pills in her handbag when we are out.

When she has done something minor that I dislike as a warning I will ask her if she could pass me the indigestion tablets,  this shows her, she annoying  me  & is getting close to a punishment.  E.g. Talking over me and butting in on my conversation.
If she does or something that has earned her a punishment I will ask her for the headache tablets & then she knows when we get home there will be trouble and sitting is going to be uncomfortable.

This I feel is a great way of letting her know and keeping it private.  Of course I do not take the tablets I drop them in my pocket,