Why wouldn't Aleksey bring Joy with him?
Alexei was still hurt from sledding downstairs and couldn't walk so Nicholas had to carry him. The dog would have had to follow along, and maybe she didn't and they thought they'd get her later with their things. Or maybe the dog sensed danger and refused to go into the room?
I have heard stories about Ortino, and even Jemmy, being killed for barking at the Bolsheviks and snapping at their legs. It would make sense if all the dogs did this, since dogs are so protective of their owners and their owners were in danger.
BTW is that a Tazmainian Tiger on your sig? Don't you think they should take specimens from the stuffed ones and try to clone them? They were the coolest things, dog's head and bark, tiger body and tail, but their jaws were like a crocodile but they were marsupials. What a unique animal. People are so ignorant to kill them all, just like passenger pigeons and great auks.