Around Hiram's barn
Solution 1:
As a British English speaker, and having grown up near Sherwood Forest[1], where, legend has it, Robin Hood lived with his "Merry Men", I have never heard the phrase: it seems to be American.
https://wordhistories.net/2018/12/05/robin-hoods-barn/ gives:
"The earliest known use of Robin Hood’s barn is from a letter written in 1797 by the American book agent and author Mason Locke Weems (1759-1825)—I could not determine whether he used the phrase literally or figuratively, as I could not consult the letter:
[as quoted in the Oxford English Dictionary (3rd edition, 2010)]
1797 M. L. Weems in P. L. Ford Mason Locke Weems (1929) II. 77 I can sell them abundantly fast without the trouble of going round Robin Hood’s barn.
Phrases.org has this credible explanation at https://www.phrases.org.uk/bulletin_board/5/messages/1405.html
ALL AROUND ROBIN HOOD'S BARN - "Robin Hood (or 'Robert of the wood,' as some have explained the name) may have been altogether a legendary figure or may have actually existed. No one knows. The earliest literary reference to him is in Langland's 'Piers Plowman,' written about 1377. He may have lived, according to some light evidence, toward the latter part of the twelfth century. But Robin Hood's house was Sherwood Forest; its roof the leaves and branches. His dinner was the king's deer; his wealth the purses of hapless travelers. What need had he of a barn, and how was it laid out if to go around it means, as the use of the phrase implies, a rambling roundabout course? The explanation is simple. He had no barn. His granary, when he had need of one, was the cornfields of the neighborhood. To go around his barn was to make a circuitous route around the neighborhood fields." From "A Hog on Ice" (1948, Harper & Row) by Charles Earle Funk. This is one in a series of four books by Mr. Funk now available in one volume.
(My reading of this is that Sherwood Forest itself was "Robin Hood's Barn" as it was where everything that Robin Hood needed was kept.) The article continues with a demonstration that "Robin Hood's barn" can be replaced by any place that was a long way away from the intended end point. This supports Spagirl's comment above.
The article continues:
Here's a colorful phrase known only to folks around Raleigh County in southern West Virginia: "I had to go all the way to Egery and back to get that." "Egery" referring to Egeria, a little community WAY out in the country close to Flat Top, West Virginia.
[1]https://en.wikipedia.org/wiki/Sherwood_Forest
Solution 2:
It may or may not be relevant to the expression that you ask about, but Frederick Cassidy & Joan Hall, Dictionary of Regional English, volume 2 (1991) has this entry for the word Hiram:
Hiram n ... Sense[:] A rustic—also used as a contemptuous term of address. [Cited occurrences:] 1939 [Godfrey] Irwin Amer[ican] Tramp and Underworld Slang] 99, Hiram.—Many of the old time yeggs [=tramp thieves] preyed upon the country post offices in the districts populated by farmers or, traditionally, "Hirams." 1932 Faulkner, Light in August 172 M[ississippi], You better go back to the farm, Hiram. 1942 [Lester] Berrey [& Melvin] Van den Bark Amer[ican] Thesaurus of] Slang 391.3, Rustic; Bumpkin... Hiram.
Evidently, in at least some parts of the U.S. during at least some part of the twentieth century, "Hiram" was a generic quasi-name assigned to a farmer, conveying the sense "country bumpkin." That being the case, "Hiram's barn" might be a hypothetical barn in a remote rural area—and "going around Hiram's barn" might imply going far out of one's way to get somewhere instead of taking a more direct and logical route.
I don't know whether this rustic sense of Hiram is central to the expression "go around Hiram's barn"—but it might be. And if anyone could be expected to own a barn way out in the middle of nowhere, it would be Hiram.
Solution 3:
I don't think that it matters whose barn, or, when you go around it. There is the phrase, "Go around the barn."
https://www.thesaurus.com/browse/go%20around%20the%20barn
Specifically, "Valeriy 2010-01-12 09:02:40 I have found some comments abt "all around Robin Hood's barn" @ phrases.org.uk: "Robin Hood (or 'Robert of the wood,' as some have explained the name) may have been altogether a legendary figure or may have actually existed. No one knows. The earliest literary reference to him is in Langland's 'Piers Plowman,' written about 1377. He may have lived, according to some light evidence, toward the latter part of the twelfth century. But Robin Hood's house was Sherwood Forest; its roof the leaves and branches. His dinner was the king's deer; his wealth the purses of hapless travelers. What need had he of a barn, and how was it laid out if to go around it means, as the use of the phrase implies, a rambling roundabout course?
The explanation is simple. He had no barn. His granary, when he had need of one, was the cornfields of the neighborhood. To go around his barn was to make a circuitous route around the neighborhood fields." From "A Hog on Ice" (1948, Harper & Row) by Charles Earle Funk. This is one in a series of four books by Mr. Funk now available in one volume.
Here's a colorful phrase known only to folks around Raleigh County in southern West Virginia: "I had to go all the way to Egery and back to get that." "Egery" referring to Egeria, a little community WAY out in the country close to Flat Top, West Virginia."
http://www.english-slang.com/eng/more_expressions/go-around-the-barn-at-high-noon
Solution 4:
Your daughter seems to be correct. I have never heard the expression myself. Hiram's or Robin Hood's barn.
https://dictionary.cambridge.org/us/dictionary/english/around-robin-hood-s-barn