Over the past two years, the former White House correspondent of Bloomberg News has interviewed more than 200 staff members and aides (many of them being surprisingly outspoken) and ploughed through files of previously unread correspondence between the world's most elite sorority - from Bess Wallace Truman and Lady Bird Johnson to Nancy Reagan and Jackie Kennedy, through to Michelle Obama - in order to uncover the truth behind the sisterly spin.
Although Brower details antagonisms between Rosalynn Carter and Betty Ford, Barbara Bush and Clinton ("who had the worst relationship of them all"), it's the revelations made about Hillary and Michelle's rapport ("probably second-worst") that have been making headlines on both sides of the pond.
"Fraught with hurt feelings and resentment" is how the author sums up the women's relationship today, confirming what White House staff have known for years.
Much of that resentment stems from 2008, when Hillary Clinton, running for the Democrat nomination, mocked Obama's message of hope at a rally in Ohio: "I could stand up here and say, 'Let's just get everybody together. Let's get unified. The sky will open, the light will come down, celestial choirs will be singing, and everyone will know that we should do the right thing, and the world would be perfect' ..." When her husband drew clumsy comparisons between Barack Obama and Jesse Jackson, Brower's book makes it clear that there's a lot more to the rift than political folklore would have us believe.
One of Obama's former aides told Brower: "When Michelle Obama views the Clintons, I don't want to say she's looking down her nose at them - but she kind of is."
The reason? "The Obamas think that more could have been done in Clinton's White House if it weren't for President Clinton's personal life," Brower reveals.
"The Obamas see themselves as people who are fighting for causes and ideals, not for money and power - which is how they see the Clintons. Hillary can't wait to come back to the White House, but Michelle can't wait to leave."
The two may not be the only First Ladies to have very different characters and motivations, but it does seem that there has been little attempt on either side to cover up this animosity. In the entire time Hillary was Secretary of State and frequently meeting with the President, no couple dinners were scheduled at Obama's White House. And despite being handed binders about Save America's Treasures - a programme started by the the former First Lady to help preserve historic sites - in the hope that Mrs Obama would help it flourish with her support, "Michelle did not feel any such obligation," says Brower. "She did not prioritise the programme, which has since lost its funding."
In the book, Obama's former personal assistant, Reggie Love, talks candidly about the First Lady's frustration at being made to give up her $275,000 a year job [as vice-president of external affairs at the University of Chicago Medical Center].
"Michelle is desperate to get her privacy and her career back," adds Brower. "What she and Barack really want is personal economic stability. She's
also still sore about all the nasty things Hillary said [in the 2008 primaries] and she doesn't like politics. I don't even think she particularly wanted to be First Lady: for Michelle, it's always been about her husband's exceptionalism."
A more consummate politician than Hillary Clinton, however - with all that the word implies - is hard to imagine. She was the only First Lady to insist on having her office in the West Wing, rather than the East, where every other president's wife has been situated, "only later realising how bad that looked", says Brower.
By contrast, Michelle Obama spends as little time in the West Wing as possible. "Maybe she was there once because we were doing a photoshoot," says Anita Dunn, President Obama's former communications director. "Besides that, she never came over there. She just didn't."
Michelle Obama was never offered up as part of a "buy one, get one free" deal, like that touted for years by the Clintons; this election, Bill is implicitly being offered up as "co-president".
Although the current First Lady feels strongly about gun control, she actively doesn't want to be involved in the day-to-day issues consuming the West Wing. ("The notion of sitting around the table with a set of policy advisers - no offence - makes me yawn," Michelle has said.) Sources in Brower's book make it clear that she has neither the understanding nor the respect for the administration's smooth turning machinery that Hillary once did.
"Hillary read up a lot on the First Ladies who came before her," Brower tells me, "whereas I think Michelle sees herself as apart from them because she's the first African-American First Lady. It is especially hard for her; anything she says is picked apart. Whether or not you can call it racism, I couldn't say.
"The Obamas are treated differently to a white First Family. The 'you lie!' comment made by Representative Joe Wilson at President Obama's 2009 joint session to Congress was something we have never seen before. And I do think that we are in more emotionally and ideologically charged political times now than any time in modern history."
For all their obvious disparities, these two fractious First Ladies do have certain similarities. For one thing, although "fashion, glamour and looks are less important to Hillary than to Michelle" - who, we are told, works out for 90 minutes, five days a week - both women have always resented the emphasis on their appearance. In the book, Michelle Obama's hairstylist, Michael Flowers, recounts how annoyed she was when aides decided that the highlights she had before the 2008 campaign were "too racy" for a potential First Lady. And, of course, Hillary has always been viciously mocked for her style choices, from the Coke-can glasses she wore back in the Arkansas days to the embroidered jackets and primary-coloured pantsuits that have had her topping "Worst Dressed" polls for years.
Another thing they have in common, points out Brower, is "how extremely seriously they take motherhood".
"When Hillary asked Jackie Kennedy for advice on parenting, Jackie told her: 'Don't let the butlers and maids spoil Chelsea - let her make her bed." Everyone who works for Michelle has said that she is very consistent on that, too. I was told that Sasha and Malia make their own beds and are very respectful to the staff, just as Chelsea was, so both women have brought up respectful girls in the White House."
They are also feminists - although it's irksome to Hillary that Michelle refuses to describe herself as such. "Michelle always brushes it off by saying she 'doesn't believe in labels'," says Brower, "which is shocking, because obviously Michelle is a feminist. Everything she has done in her life - going to Princeton and Harvard and becoming a powerful lawyer and her policy work - tells us that."
It's also harder to imagine Michelle Obama going along with the "bargain some of these women strike with their husbands to keep quiet about infidelity" that Brower writes about in the book. Because it wasn't just Clinton and Kennedy who philandered their way through their presidencies. President Johnson made no secret of his affairs - and Lady Bird Johnson famously admitted to Barbara Walters that "Lyndon was a people-lover. And that certainly did not exclude half the people of the world, women."
"I don't think President Obama could get away with cheating on Michelle," laughs Brower. "Partly because theirs seems to be more of a genuine relationship than the transactional one we see between the Clintons. But also - and, as a White House reporter, we would always joke about this - anyone would be terrified of cheating on Michelle. She may not call herself a feminist, but if faced with a similar situation to the one Hillary endured with Monica Lewinsky, I think she would behave in far more feminist way."
Whatever their fortunes hold in store, these two members of the 1600 Club will one day find themselves in the same room again. They will grin and bear it for the cameras, of course, but given what we now know, it seems unlikely that they could bond over anything - except, perhaps, the mutual dismay they would both feel were the First Lady baton to be handed down to Melania Trump.
"I assume they would both be stunned. No matter how bad things have got on campaign trails, no one has ever questioned a president's citizenship before," says Brower, alluding to the public pursuit of Obama's birth certificate by Trump back in 2011.
"What Trump said about Barack Obama is so much worse than anything that has ever been said on the campaign trail before. And maybe Michelle would say that Melania is not to blame for her husband's actions, but one thing's for sure: if that transition were to happen, it would be one very awkward introductory tour of the White House."
First Women: The Grace and Power of America's Modern First Ladies by Kate Andersen Brower (Harper) is published as an e-book on Thursday ($16) and available in hardback on May 30 ($50).
