I managed to get Daphne in the carrier rather easily. I just swooped her up and carried her in the garage. Zoe somehow figured out we were going to the vet -- even before Daphne had been spirited away. She wedged herself under our king-sized bed - right in the middle so she couldn't be grabbed from either side. For 30 minutes, we tried to coax her out. Finally, it was time to pull out the big guns. Simon placed a trail of treats on his side, I poked her butt with a plastic coat hanger on the other side. Finally, Simon was able to grab her.
When we got to the vet, Daphne attacked Zoe in the carrier. That was special. When we got in the room, she attacked her again. Luckily, I brought another carrier so I put Zoe in that one. While pulling Zoe out, I managed to get clawed by Daphne as I tried to protect Zoe from the swatting mitten paw.
As we waited, Zoe sat quietly in her carrier. Daphne growled, hissed, swatted and made a nuisance of herself. The vet started with Daphne, since she was the angriest. They couldn't get her out of the carrier. They even tried to turn it vertically so she could shake her out. No go. Finally, they decided to take the carrier apart. At this point, Daphne freaked out.
They decided to take her in the back where they take all the bad cats. They tried to cover her with the towel from the carrier. Daphne freaked out again, thrashing, flailing, hissing, swatting. She broke free and started running around the room.
At this point, the vet bailed on Daphne and worked on Zoe. Daphne celebrated by sitting in a corner and hissing at everyone. Zoe does not enjoy the vet either. However, she expressed her displeasure by going limp instead of acting like she's been possessed by a demon.
Finally, the vet asked Simon and me to wait in the waiting room with Zoe. Apparently, they had to muzzle Daphne so she wouldn't bite them. Luckily, both of the girls are in perfect health. Pictured on the right is a picture of what a cat muzzle looks like.
Here's a YouTube video that demonstrates what Daphne was like -- except there was no net involved.