Thearesia van Astrea
In their youth, Wilhelm was angry at Thearesia for hiding her identity as the Sword Saint. He took that as her looking down on him and his swordsmanship. However, after finally defeating her, he declared that he would take the sword in her name, so that she wouldn't be forced to fight anymore to protect her loved ones. In their latter years, Wilhelm came to deeply love his wife, as he even took her surname van Astrea despite his initial dislike of the Sword Saint's lineage. After her death during the Hakugei expedition, Wilhelm was motivated by his desire for vengeance on the Hakugei.
Heinkel Astrea
Wilhelm's relationship with his son is heavily strained, especially since his wife died while on the Hakugei expedition, something that she took on because Heinkel refused to do so.
Reinhard van Astrea
Wilhelm's relationship with his grandson is very tense, likely because Reinhard inherited his wife's power as the sword saint just before she died, making her much weaker than she was at her prime. Nevertheless, Wilhelm did want to fix their relationship after the Hakugei was successfully killed. However, after Reinhard was forced to kill Thearesia's resurrected corpse, Wilhelm asked his grandson if he had any regret doing so. After hearing Reinhard's answer, he begins calling the current Sword Saint by his full name, showing that he sees him now as a stranger rather than his grandson.