Erica Howton maybe I can save you time, stress & nervousness (maybe more mine:)
well in reality she has already been examined by the serious ones of:
-https://www.wikitree.com/wiki/Hohenstaufen-71 <--{isolated}
Research Notes
There is no proof that she is the daughter of either Hohenstaufen-35 and Hohenstaufen-69. Her father was removed 7/11/21. The link below to a discussion on the soc genealogy medieval discussion group proposes she actually never existed and is not mentioned in any primary sources of the period. They also make the point that the name Franziska/Francesca/Francoise didn't exist in any royal/noble family in this time period. There is no known any primary source for Thomas of Aquino's grandmother. The Aquino family is considered of Langobard stock and not originally Southern Italian. They were a Germanic tribe with close ties and frequent marriages of their rulers to the Bavarians.
Sources
*https://groups.google.com/forum/m/#!msg/soc.genealogy.medieval/4cwJ...
*https://www.ourfamtree.org/browse.php/Aimone-I-Conte-d-Aquino/f31467
*www.ourfamtree.org /browse.plp?fid-10110
If Francesca (born 1137) was daughter of Hohenstaufer-35 ( Holy Emperor Friedrich I Barbarossa she should be daughter of Bourgogne-270 (born 1131) that is not possible.
Francesca/ Frances/ Françoise was daughter of Frederik II (single eye) duke of Schwabia 2nd wife Agnes of Saarbrucken, while Frederik I Barbarossa, Holy roman Emperor was half brother of Francesca and was born from his first wife Judith of Bavaria, duchess of Scwabia. If this is the case, all siblings shall also be edited.
It is not clear how she married Aimone d'Aquino of neapolitan origin. Of couse she could not be the wife of Rinaldo d'Aquino's father of Aimone that was the spouse of the ill-documented Cecilia di Medania. Her (only?) child was Landolfo d'Aquino who married Teodora Caracciolo (or according to other sources Teodora Gallucci) having among his twelve children Saint Thommaso d'Aquino , one of the leadinng Catholic Church Saints. Not much else is documented about Francesca's life.
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Also be careful because I followed the trail that led to her project:
-https://www.geni.com/projects/Distinguished-Matriarchs-of-Noble-Blo...
and the amount of profiles completely blank empty but colored with nice colored COAs... from the usual ones I know now, there are many many many and I only stopped at the first pages.