Yeah there is very scarce info about the last Bourbon Royal Family, at least in English. For instance, some of the journals of Henri V were published a few years ago in French. It really makes me want to learn French. But most of the Info I have about him is from Marie-Therese by Susan Nagel. Its the only modern biography I've been able to find on Madame Royale. But apparently she didn't try to persuade Louis XIX to keep the throne. She wanted Henri V on the throne and sort of got her way, for 5 days at least. And the coldness was also misreported. She was very vibrant to close friends and apparently had a great sense of humor. But yes she was very distant in Public and never felt comfortable in Paris. Which is understandable considering what happened to her family. But yes she was very conservative, though even Madame thought Charles X went too far, and was the primary reason of the Duc de Bordeaux's conservatism.
Yes, I have that book on Madame Royale! It's the only thing in English on her actually. There are some older things in English in google books that I could recommend. The French Restoration is one of my interests, French history in general but the Restoration especially is interesting, and the end of the ancien regime.
Ones that come to mind are
The Private Life of Marie Antoinette, Madame Campans Memoirs,
The History of the Restoration in France by Alphonse de Lamartine in 4 Volumes,
The Duchess of Berry and the Revolution of 1830, The Duchess of Berry and the Court of Charles X, Charles the Tenth and Louis Philippe, The Duchess of Berry and the Court of Louis XVIII.
These can all be found on google books, are within the public domain as are usually issues from the 19th century or early twentieth, and completely free to download to your account and read from your computer or phone/whatever through google play. I have TONS of history books in the public domain on tons of subjects, the courts of Louis XIV, XV, and XVI, Charlotte of Wales herself, Elizabeth I, Mary Stuart.... ect, all free. One thing to keep in mind is they aren't modern literature, so can hold biases of the period they were written, will not contain new information, but they are in English, and on subjects such as the Restoration, have lots of stuff, considering that period isn't well covered in English. Susan Nagel's book was only released back in 2011? And there's virtually nothing on Louis XVIII and Charles X, except in broad books that cover 19th century century history. Same goes for Charlotte, there are lots of memoirs with info on her, you can get the memoir of her companion Miss Knight. It's all helpful, has information, and in many ways is more personal. The books of the Duchess of Berry concerning the Courts of Louis XVIII and Charles X have tons of information on the personal life of the Duchess during her short marriage and her life following Berri's assassination and how the court functioned. There's some political info (I think the book concerning the Duchess of Berry and the Revolution of 1830 would have more of that, but I've only scanned it. I did read the first volume of the series, of the Duchess and Louis XVIII's court and loved it.)
But you hit the nail on the head. Cold in public; there were retorts on the Bourbons return to Paris that she was very cold, but around her family she was very nice. No doubt returning to France was traumatizing, but she did love the country: there's a reason why she married Angoulême and not the Archduke Charles. It was her mother's wish as she didn't want her daughter to leave the country, even though Louis XVIII tricked her. Angoulême wrote her love letters prior to their meeting, but they were actually written by Provence. But she still married him, and despite his stuttering and supposed impotence (which was apparently not true, as she miscarried during their English and exile and I've heard of a second pregnancy during the Restoration, but it was actually the onset of menopause), they got along and became friends.
There's a reason why Napoleon called her the only man in her family, too. Her actions in Bordeaux were very brave, she intended to stand up to Napoleon; it was only when the troops in the city said they would not intervene or fight against him, that she left. She probably felt that the French people were "ungrateful" in a sense towards her family upon their return.
There's also the fact that the 1820s was filled with men claiming to be her brother, the shallow graves of her parents being uncovered... it would be mentally straining on anyone. She even apparently met with the wife of her brother's goaler, the cruel shoemaker who made would get him drunk and make him sing revolutionary songs, ect. The woman was old at this point, and told Madame Royale her brother was not dead, had indeed been switched out... I think Susan's book covers it, but I don't recall. But all the claimants claiming to be her brother, it was hard on her. She never admitted he was dead, but she never claimed that her uncle was usurping the crown, and supported Chambord's claim.