This argument is further supported by the replacement by Andrew I of Hungary (husband of Anastasia of Kiev) of his brother Béla as his heir apparent with his young son Salomon in 1057. If Agatha had been Andrew's sister-in-law, and aunt of Salomon, this act by King Andrew would have strengthened her bonds and those of her husband Edward to Hungary's future: however, if Agatha was a sister-in-law to Béla (husband of Richeza of Poland) she and Edward would most likely have been inclined to leave Hungary in 1057 at the time of Béla's rebellion.
This argument is further supported by the substitution of Andrew I of Hungary's brother, Béla, with his son Salomon as heir apparent in 1057. If Agatha was a sister-in-law to both Andrew and Salomon, this would have strengthened her ties to Hungary. However, if she were related to Béla (husband of Richeza of Poland), Edward and Agatha might have left Hungary during Béla's rebellion.