Your reaction to your pets being at the vets is normal. Although I have misgivings about leaving them alone for overnight, my fears are only allayed when I pick them up early the next morning.
I think when cats are in pain or discomfort, their natural instincts is to be alone. When I had Chrissie and Happy cat neutered, they were OK on the way to the vets, but bringing them home we had to separate the two of them into separate carriers. Chrissie was so weak with anesthesia, all he woud do in the carrier was lay down, while Happy cat kept attacking him. I have never seen these two have a disagreement nor a squabble, but instead they often play together.