It is ok to use the word breast. Why is two to old?
Usually by two, they have teeth and should be eating solid foods.
Babies usually start on pureed foods at about 6-7 months, but that doesn’t make nursing irrelevant. It is by far the best kid-quieter in the world, short of narcotic sedation.
I once breastfed my son at age 2 when husband and kid and I flew cross-continent. I did not make an issue of it, had a nicely-contructed, modest nursing outfit on; and the only thing anybody “noticed” was that here was a child who went through take-off, hours of flight, and landing without running around, squirming, or screaming.
Nursing moms whose whose toddlers’ nutritional requirements are met by other foods, still often nurse at night for peaceful bedtimes.
Having made that point, let me also say that this Vermont mom didn’t handle things very well. She should have smiled, said “Oh, Thank You!”, accepted the blankie, and made some reasonable gesture of cooperation. I doubt anybody would have raised any further objections if all were thereafter blessedly peaceful and quiet.