Run fast. Don't look back. Never do business with them again.

As for the interior designer...let her and your competitor provide the chairs at the "lower price". Bill hourly (consulting) whenever she asks you a question about them. Include any time already spent.

Or just tell the client what cost on the chairs...making it impossible for the ID to mark them up. I would sell seating from someone else at cost plus installation just to spite all three of them. (ID, competitor and manufacturer)