Swap Sets/Triggers in Child Puppet not working in Parent Puppet

I have a puppet that I partially modeled off the Brooklyn Buddies Bunny puppet, in that there is a shared Head puppet used to create head positions (left quarter, front, right quarter) and other facial expressions (eyebrows, etc.). This Head puppet is used three times in my parent puppet, once for each of the body views (right profile, left profile, frontal).

When the Head puppet is added to a scene by itself, all of its swap sets and triggers work perfectly. However, when the parent puppet, containing the Heads is in a scene, the swap sets and triggers do not seem to do anything.

The Head puppet has its own Triggers behavior. I have made sure that all Triggers behaviors are armed in Record mode. Even using the Controls Panel, there is no response. All swap sets and triggers for the parent puppet work fine.

One thing I've noticed in the Bunny puppet is that the swap sets for the child Head and Arm puppets also appear in the Triggers panel for the parent puppet. Mine do not, and I can't find a way to duplicate them there.

Any ideas or suggestions for things I can try? Thank you!