If the assistant truly feels they can do better, they should be interviewing for other HBD jobs.

The principal (and/or fine arts admin) has decided that the HBD is the one to lead the program. If the assistant isn't willing to be led, they need to get out of the way and go work somewhere else.

Every single thing you hear, every single thing you see - document, document, document. Keep a notebook. It may be that the HBD knows what's going on but is attempting to be the professional one and not stoop to the ABD's level. But this is easily grounds for a reassignment to another campus, since our contracts are with a district, not to be "assistant director at XX High School" after all.

Furthermore, by not raising objections to their insubordination and undermining, you could be interpreted as giving tacit acceptance to their point of view. Even a simple "This is not a discussion we need to be having" is enough to deflect here.

You need to protect YOURSELF first in these situations. Pardon the expression, but sh!t rolls downhill. Careful you don't get covered in it when it hits the fan. I'd also polish up your resume just in case - in situations like this, it's not unheard of for EVERYONE to get blown out of town within a year or two as admin gets tired of the drama and wants a clean slate.