Llywelyn Fawr was married several times, albeit of dubious legality, something never mentioned in Penman's novel (she seems to have had no knowledge of any of his wives, aside from his concubine, Tangwystl). About 1191, he requested the hand of a daughter of King Raghnall IV of Man. A papal inquiry into this whole complicated matter helpfully sheds some light on all this. It seems that this Manx princess (never named) was aged eight in 1191 when the betrothal was sought, but Raghnall did not send her to Wales at the time appointed, so Llywelyn instead married a sister of the earl of Chester (probably referring to Ranulf, earl of Chester). So instead the Manx princess married Llywelyn's uncle Rhodri ab Owain, who then died in 1195. By 1199 Llywelyn's Chester wife (also never named) had seemingly died, as he tried to marry his uncle's widowed wife, the Manx princess. Pope Innocent III determined that any marriage between them was illegal due to her having been his uncle's wife. This matter was argued over from 1199 to 1205, when Llywelyn abruptly dropped the matter, as he had received a much more attractive offer: King John's illegitimate daughter, Joan.
According to the Worcester Annals, Joan and Llywelyn were married at Ascensiontide 1206, so they would've married in mid-May 1206, according to the helpful Medieval Calendar. The only hint we have to Joan's age is the papal decree of Honorius III legitimizing her, which claims that King John was unmarried when he begot her. John married his cousin Isabel of Gloucester in 1189, and then dissolved their marriage in 1199. If the papal decree is correct, then Joan was probably born in the mid-to-late 1180s, before John's marriage to Isabel. Expenses for John's daughter Joan were recorded in Normany in 1203; this almost certainly refers to the illegitimate Joan, although G.R. Stephens thinks it's her legitimate half-sister with the same name (G.R. Stephens, The Early Life of Joan Makepeace, Speculum 20, 1945).
Who was Joan's mother? Penman invents a character named Clemence d'Arcy, a well-born Norman girl impregnated by John and then cast off, who dies in alcoholic misery. The only source that explicitly names Joan's mother is her obit in the Tewkesbury Annals: Obiit domina Johanna domina Walliae, uxor Lewelini filia regis Johannis et regina Clemencie, iii. kal. Aprilis."
Who was this Queen Clemence? The title "queen" seems to have been a respectful term from the monk. The only Queen Clemence in Europe at that time was Clemence of Toulouse, wife of Sancho VII of Navarre, and it seems doubtful that John had a liaison with such a prominant woman without some mention being made of it.
A much more likely candidate is Clemence, wife of Nicholas de Verdun. From the Patent Rolls of the Reign of Henry III comes this entry from 1228, from King Henry III (son of King John and thusly Joan's half-brother):
Rex dilecto et fideli suo Nicholao de Verdun et Clementie uxori sue, salutem. Sciatis quod nos vobis benigne concedimus quod fidelis noster et dilectus frater L. princeps Norwallie et Johanna uxor sua et dilecta soror nostra Susannam filiam suam, neptem nostram, vobis committere duxerit [sic] nutriendam, eam salvo et secure et sine omni dampno et occasione suscipiatis et penes vos retineatis. In cujus rei testimonium etc. vobis mittimus. Teste me, apud Westmonasterium, xxiiij die Novembris, anno etc.
Henry III is placing his niece Susanna, the daughter of Llywelyn and Joan, in the care of Nicholas de Verdun and his wife Clemence. This entry is worth a second look. We know Joan's mother was named Clemence. Here we see Joan's daughter being placed in the care of a woman named Clemence, who is a subject to the English king. If Clemence was Joan's mother, she would've had an obvious interest in her granddaughter Susanna.
Clemence was the daughter of Philip le Boteler (Curia Regis Roll, 1243 [17:281-2 (no. 1462)]) and she inherited lands in Steeple Lavington, Wiltshire that she later bestowed upon another granddaughter. She and Nicholas de Verdun had one known daughter and heiress, Rohese. Rohese de Verdun, in turn, married William Perceval de Somery (died by June 1222) by whom she had a son, Nicholas (died a minor before 4 July 1229; his heir was his uncle Roger de Somery). Rohese then married Theobald Butler in 1225, by whom she had further issue. Nicholas de Verdun died in 1231; Clemence was still alive as of October of that year, as was their daughter Rohese.
Dafydd, the son of Llywelyn by Joan, is well-attested. A daughter, Elen, is known to have inherited Joan's manors of Bidford and Suckley. This Elen was the wife of John le Scot and Robert de Quincy, respectively. Susanna is named in the 1228 patent roll. The Melrose Chronicle states that Malcolm, earl of Fife, married a daughter of Llywelyn Fawr circa 1230. Malcolm was a supporter of Henry III. The most likely candidate for his wife is Susanna, who we know was in England in 1228, and could easily have been given to Malcolm by her uncle Henry III.
Marared seems to have been Llywelyn's eldest daughter, as she was named after his mother. She married John de Braose in 1219 (Brut y Tywysogyon) and their eldest son William came of age by 1245, so he was probably born no later than 1224. Due to this chronology, she cannot be a daughter of Joan.
Gwenllian appears to have been Llywelyn's daughter by Tangwystl, and a full-sister of Gryffudd. The evidence for this comes from a letter dated 1224, written by William Marshal to King Henry III, listing the people who surrended to him after the seige of the castle of O'Realy. Among them was "uxor Wilelmi de Lascy, filia Leulini, soror Griffini de patre et matre... (Royal and Other Historial Letters Illustrative of the Reign of Henry III, vol. I, Chronicles & Memorials of Great Britain and Ireland, vol. 27, Walter Shirley). Gwenllian was the wife of William de Lacy, one of the English rebels against Henry III, and here she is clearly described as Gryffudd's sister by the same father AND mother. If she had been Joan's daughter, she would've been Henry III's niece, something William Marshal would surely have commented upon.
Gwladys Ddu was another of Llywelyn's daughters, and usually assumed to have been the offspring of Tangwystl, by Penman among others. She was betrothed to Reginald de Braose in 1215 (the father of the William who was hanged for supposedly having an affair with Joan!). They had no children and he was dead by June 1228. In 1230, she married Ralph Mortimer and by 1237 they were in possession of the manors of Knighton and Norton, which had been part of Joan's maritagium. If Gwladys was a daughter of Joan, she would've been a young child when she married Reginald de Braose and, at most, twenty when widowed. This would explain why they had no children during the long years of their marriage. She and Ralph then went on to have several children, including a daughter named Joan and a son named John. These names strongly suggest that she was Joan's daughter. Also, in 1229, Gwladys journeyed to London to support her brother Dafydd when he was recognized by the English crown as Llywelyn's heir. Why would Gwladys support a half-brother over Gryffudd, supposedly her full-brother by Tangwystl? The simplest explanation is that Gwladys was Joan's daughter, thusly explaining her support of Dafydd, the Norman names of her children, the many childless years with Reginald de Braose, and her inheritance of Joan's manors.
From this evidence, it would seem that Joan and Llywelyn's children were: