[@MrDidact] The character's named are all in running for the Frey seat those with other families names are still from Walder's genealogy, but are minor houses rarely mentioned in the books. Steffon the second is the son of Walder's Grandson Steffon the first through Walder's second wife. Jenn rivers is a bastard born grandchild of black walder. Mable and Malkor are children of Bryan Frey. Walder Haigh and Rickard Wylde are great grandchildren of Walder Frey as well through his forth and fifth wife. I only meant in the deaths to imply the first wife's descendants had killed each other off as well as the grandparents. In a family tree this complicated it ends up that most houses have some connection to the Frey House. I'll remove Walder Haigh and Rickard Wylde to simplify my sheet. If anyone wants to be a frey there are still 68 other great grand children or more who could try to claim Riverrun my focus is on Malakor and Mable only because Malakor managed to retake Riverrun temporarily. Jeffon is the proper successor after the blood bath, but almost all claims are weak. Jeffon is therefore not only attempting to clear the lands of Malakor, but stop any challenges to his position. 

Thanks for your patience with my CS I never realized how hard it would be to make sense of the Frey family tree. Indeed the Vance house has a stronger claim to riverrun then the Frey's.