I think I might have one of the gods position on the tree switched. Not sure. But this is as close to an explanation of the relations between the gods I can come up with.
You are forgetting a few relationships.
In the original 3.0 Codex Arcanis it states that
Beltine, is the sister of Saluwe (pg 7)
Saluwe is the sister of Beltine and Althares (pg 6)
Althares is the sister to Saluwe and Beltine (pg 7)
While Althares being female could be a typo, because later in the description is does say “he”. I believe the rest is accurate.