Pepin the Hunchaback wasn't illegitimate son... For the frank law, fredelehe, temporay civil marriage, gave at the son the same inheritance rights of catholic marriage.
Charle Magne was born in fredelehe. Rodthaid born of a concubine "more danico", for the frank law was not entitled to inherit
For what mattered, aka succession to a throne and to a family that based his power to the respect, support and leadership of Christianity, they were considered as illegitimate, because Christian elites didn't know anything but one spouse. Period.
It's why Pepin couldn't repudiate her and didn't dared to do so after the papal interdiction.
Furthermore, I don't see something about Bertha being a friedelfrau. Arguably, the system is far for being the consistency and the institutionalization you give him and it's difficult to make a definitive statement. (BTW, the marriage "more danico" is something else, while related)
According to Michel Rouche (one of the specialist of the period) : one spouse had the first rank, which was considered as the true spouse by the Church, and the others were considered as second rank spouses (mere concubines, still for the Church)
For Bertaldra, I simply didn't found something about it. Could you give us a source please?
Maybe I'm a bit vague, so allow me to clarify my point : I don't deny that according germanic institutions, sons from a friedlehele could inherit fully. Charles Martel was such (but had nevertheless to fight during 4 years to support his claim).
But as Pippinids based their overthrowing of Merovingian on the collective blessing of Pepin and his descendants by the pope, I think the successor should have been a legitimate one according to Christian and Roman standards.
a: if Pippin, as in our TL, died in 775 who becomes frank king ?
I don't see why he should dies on the same date. His death was arguably due to how his uncle, Charlemagne, treated him : being cloistered doesn't help to good wealth.
Now, if he dies early : probably Pepin the Hunchback, born circa 770. Desiderata of Lombardy being repudiated, Pepin would have been in a vague situation where he would have been the most legitimate descendant of Pepin III. Admittedly, it wouldn't go without troubles in Francia.
b: to some historians, Rodthaid is a woman (CHROTHAIS in other transcription or one of unnamed daughter... Paulus Diaconus wrote a poem in memory of "Rothaidis filiæ Pippini regis", but it could also be a mistake of the copyist, because in some annals is quoted as man )
If he was a man, he would certainly have inherited part of Francia.
Furthermore, Rodthaid is a name used by other women : Rodthaid of Bobbio, spouse of a Pepin of a minor branch of Carolingians, using the same Chrothais variance.
I don't think that such name can pass from masculine to feminine even in 100 years.
When these annals were made? If they are quite close of the late VIII/early XI, it could be interesting. If not, I would be tempted they are the result of a copyist mistake
