Calming a Cat Going to the Vet?

One of my two cats has to go to the vet. Problem is she doesn't initially like strangers, it takes her a little bit to get warmed up to them, and I've never had one just try to grab her and pick her up right away. I don't think that would go over too good. However, she does let us pick her up. The other cat, her sister, absolutely hates being picked up no matter who it is. And their mom, who was a stray that was mildly feral when we took her in, also wouldn't let you pick her up. Luckily the one that has to go to the vet is the easier one to handle but still this is going to be a stranger instantly grabbing at her somewhere that she never has been, shes an indoor cat so her world is very much our house only.

Any ideas or tips on how to make this process less crazy? How to make her feel better, soothe, or calm her down so she can actually be handled by the vet?

There are actually calming aids you can try.  Calming collars, calming sprays for her carrier, Bach's Rescue Remedy for Pets, which can be applied to her footpads or rubbed in her ears, or ingested if you can get her to eat a treat with a few drops on it. 

Will she go into the carrier and take a ride without getting too freaked out?   If not, try playing harp music on the radio or CD player in your car, and cover the carrier with a towel.  I don't know how soon you'll be going, but if you have time to prepare her, here is a great article to prepare her for the trip:  http://www.thecatsite.com/a/beware-the-dreaded-cat-carrier

Otherwise, as far as when she gets to the Vet, just tell them she is extremely fearful of strangers, and let them take the lead.  I'm sure the Vet is used to dealing with that situation.  Believe me, you are not the only one who has a "shy"  scaredy cat .  Where do you think that phrase came from