Assuming this is true, (and given the excellent references from early Church sources, it probably is true) where does Zebedee fit into this family tree? I don’t think he does. Still, it is irrelevant.
The fact that James and John were referred to as brothers of Jesus is not understood if translate literally. One of the problems with the colloquial Aramaic use of ‘‘brother’’ is that it was used for brother or any level of distant cousin. Eusibius, who wrote in Greek, used more precise language but was interpreting 200 year old documents. So to understand the new testaments’ meaning, you have to look at the whole New Testament’s descriptions of family relations.
One thing we know is that when a woman lost all her sons, she was consigned to a life of begging. We also know that sons were obligated to care for their mothers, but not necessarily other relations. If Mary had sons other than Jesus, He would not have needed to give her to John. In fact, Jesus giving His Mother to an outsider or a distant relation when there were sons to care for her would have resulted in bad feeling and probably even a huge riff between the sons of Joseph and the sons of Zebedee. No such struggle took place because Mary, ever Virgin, gave birth to no Son except Jesus.