Most chins do not like to be handled. Out of 24 chins that i had at 1 time, only 1 was truely hand tame
They're prey animals and flight animals, so don't get too upset when they don't want to be handled, It's their natural instinct

Just a theory about they're fur, has you're vet ruled out a fungal infection?

Is the fur coming out when you hold them? That could be caused by stress. Also, a chin will literally shed patches of fur if they feel threatened. Either that or it could be fur chewing.

I would imagine that moving them from one place to another could be causing alot of stress, and that could be why they won't let you near them.

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