That is a mess! I would fight it , and be in it to WIN.
your getting screwed. Do not let them do that to you. It is under warrenty .And keep taking your claim up to the highest and highest authority figure possible, until the matter is resolved in your favor. Meanwhile keep all your dogs safe. I am certain that you will.
It has hit triple digits in California this weekend , and beyond . I can't imangine going without AC right now! My Suzi goes outside on the balcony for a min, and is running to come indoors, panting!
Best wishes to you.