player A1 controls a Eidolon of Blossoms Player A2 cast Eidolon of Countless Battles. Will constellation trigger?

My understanding is that it will not since A1 controls the creature with the ability and player A2 controls the enchantment. Constellation triggers when " or another enchantment enter the battlefield under your control.“ If the fact that it is a 2HG game changes who the ”under your control" refers to from the player to the team then I would say that it would trigger. However, it is my understanding that it does not.

Am I right or wrong, and if I'm wrong why?

It will not trigger.

In Two-Headed Giant, individual players control permanents. There are only a few cases where instead the team is considered - e.g. creatures attack teams, not players. Control of permanents is not one of these cases.

Daniel Kitachewsky
L4, Paris, France
Rules NetRep