Guess I was too long-winded to get advice?
Okay, just in case this helps anyone... we just vaccinated all cats today. And here's what I learned:
1. Mom cat -- the original stray -- will NOT like being transported. We tried introducing her to the carrier (we only got one), but in the car she was very agitated and peed. LESSON: Bring toilet paper and newspapers if you are transporting a lot of cats.
2. All kittens went into a tall cardboard box. ...They are ~2 months old... and they ALL can jump. They wanted to explore and they kept escaping. LESSON: Make sure you have more than one person to help "catch" the kittens and put them back in the box.
3. We were very lucky we found a vet near our place and was very empty. The vet let us put all the cats in his examining room and closed the door, so they can explore all over. If we had to wait in a waiting room with other dogs/cats, I think it would have been CHAOS.
When we all got back, they don't seem too traumatized. I think it helps that the kittens were socialized a lot with us, so a trip to the vet wasn't very scary. The stray cat has always been a little "cool cat" so she recovered from her trauma pretty easily.