Dappy sounds lovely, bless her, in spite of her current difficulties.
It's always hard to second guess with rescue cats, as you have no idea what triggers (if any) may have set off stress related grooming in her old home, and therefore what it is you're working with now - stress related over grooming or indeed an allergy.
Might also be worth a check up visit to the vet, so that they can rule out anything like feline mange (and it doesnt sound like that's what she has, but it cant hurt to get it ruled out). Having said that, if Dappy gets stressed by car travel or vet's visits, best to have a word with the vet first, before taking her on any unnecessary journey.
I hope you can get to the bottom of this, so that Dappy can be comfortable and entire in her wardrobe dept.