This is the book The Halfmen of O, by Maurice Gee. It is the first in a trilogy, the sequels are The Priests of Ferris, and Motherstone.
Susan has a birthmark on her arm. It looks a bit like the yin-yang symbol, but in red and gold. She and her cousin Nick meet an old man who sends Susan through a sort of portal to O (via sniffing a drug!) Nick follows her to "rescue" her, but she is very much the protagonist. Odo Cling is the bad guy, who captures Susan and starts taking her to the Darklands. (The old man is working for him, but when he wants to be paid he is killed.) Susan is then rescued by the Woodlanders (the forest people), but they are being hunted by the Bloodcats (vicious cats trained to follow the scent of someone's blood).
The Halfmen have made O dark and grey. Susan has to go to the Birdman and Stonefolk tribes to find the stones that match her birthmark and restore balance, before Otis Claw and the other Halfmen invade New Zealand through the portal.
These books came out in the 1980s and are a bit reflective of that time, though are still very good. Maurice Gee is one of NZ's most important writers, not just for his children's books, he has written widely. Some of his books were made into tv programs but they are hard to get now.