Truth be told those were some really amateur hunters.
Other than Carmen's ability to resist Sharon's mind control they first sprung the trap too soon and tried to face Dan with only melee weapons.
Sure my Dan had the claws power so i am not sure how easy this fight is without it (haven't done more than on playthrough so far). Still their original plan was to face both a "baby vampire" and a adult one (Sharon) at the same time with axes.
Still i agree that it is unlikely Carmen will die now. More likely she will be kept in the cage for now or Sharon will turn her into a thrall too.
I am more interested in the vampire who attacked Sharon and Dan's "mommy" who seems to be a really powerfull telepath.