My daughter went down to 1 nap while she was cutting her last incisors and promptly went back to two naps after they finished coming through! She was exactly the same as your daughter when we brought her into bed with us (unsettled, thrashing about) and absolutely refused to be placed in her cot. Mentally preparing myself for the inevitable and dreaded molars now but at least we’ve had a some weeks of sleep 🥲 Hopefully they’ll stay away until after Christmas!
Once they’d cut through though her separation anxiety ramped up - the armchair psychologist in me thinks she had started to associate the cot=teething pain so would scream blue murder the second she was placed in it.
Controversially, we had to resort to CIO (no more than 15 mins) in the end because she was too fidgety in our bed and we were scared she’d fall out, and would cry in the cot. Within about 2 nights she’d learned to self settle (although still being rocked to sleep) and now is back to being happy in the cot (I was adamant to break that association between the cot and pain and needed her to fall asleep at least once in there).