I had read and from my experience, believe, that animals know understand death when they see, sense and smell it, but only know "gone" when they don't have that opportunity and may feel more distressed or abandoned in the latter situation. 
 
We had one beloved cat die at home just before we came back from a wedding - we made sure the other animals saw her, sniffed and understood before taking her to be cremated.  They still mourned - Benito called out for her that night, but shifted the attention he had paid to her to us quite quickly. 
 
When we had to help Jesse out of this world, the vet came to our home and the two cats were hiding in the bedroom.  Earlier that day, we'd had her on the bed with us and both cats joined us and Iggy, for the first and only time, laid right down next to her - along her side.  He'd always been a little skittish with her, but he knew she was struggling and he cuddled close to comfort her. 
 
Later, when the vet had completed the procedure and she was gone, he came out of the bedroom on his own, walked through the group of us (vet, tech, two friends and me) to her in DH's lap and sniffed her and then looked around at us and gave a plaintive, questioning mew. My vet answered him, "Yes, she's gone," because we ALL understood that to be the question.  And it was good and right for us and peaceful and the cats were not anxious about her. 
 
I wish you strength and courage in this situation, Pomegranate, for you, Katie and Elizabeth. 
 
Is there any chance your vet would perform euthanization at your home?