I got to wondering whether other families use the expression 'barley' in this sense, and found it's not widely used.
The Virtual Linguist is collecting examples of the use of this and similar words. A Wikipedia article refers to the use of this term, with variants, in Australia.
Peter Opie, who in 1959 conducted the most extensive study on the subject to date, considered the truce term to be the most important word in a schoolchild's vocabulary and one for which there was no adult equivalent...However, research into early recorded use of these terms found examples of some of these terms being used as a sign of surrender in battle or adult fights or quarrels as late as the 18th century.It seems to me the phrase will stay in an adult's vocabulary if the adult continues to play, in the kind of innocent way children play - and, of course, that's what pet dogs teach us to do.
The Lore and Language of Schoolchildren,by Iona and Peter Opie, was published in 1959, with an introduction by Marina Warner that says, in part
In the chapter called “Code of Oral Legislation,” they give a truly mind-boggling list of over fifty “truce terms,” including variations on “barlay,” “crosses,” and “squits,” by which children “obtain respite” from one another during a fight or other kind of struggle; a gloss provided by J. R. R. Tolkien himself connects “Fains” (pronounced “Veins” at my convent school in the Sixties)
with Old French se feindre, and he is able to use it to throw light on a crux in Chaucer, making the term five hundred years old. It must be said that the beautiful “distribution maps”—no less than six in this chapter alone, here illustrating truce terms’ usage—add considerably to the impact of the data; with something of the quality of a handdrawn treasure map in an adventure story, they reach a high-water mark that published scholarship in this field will probably never attain again.
I notice the word is spelled barlay in the Opie book.
I think I'll look for a copy of the book, after reading a review of it by Kenneth Rexroth (written in 1960).