At the conference, Anne M said the main problem is that their main association is via smell, so they sort of say "you look like my friend, but you don't smell like my friend" after a bun has been at the vets, and that's what can cause the problem more than the actual separation for the day.
If you really can't take them both, I would get a towel and give him a really good rub over with it before he goes, so that his smell gets on the towel. Then when he comes back you can rub him over with it again, then rub her with it and rub it back on him, so that you transfer a bit of the 'original' smell down and minimise the 'hospital' smells.