Louise Cooper, Mirror Mirror: Breaking Through, and Mirror, Mirror: Running Free (London: Hodder Children's Books, 2000).
Cooper has produced two books which are supposed to be one book really, but actually they aren't. OK, I know that doesn't make sense.
In Mirror Mirror: Breaking Through Angel lives in a nasty super-commercial world, her mother is shallow and wants to her to Partner a boy at 15 so she doesn't have to pay for Angel's education. Running away from this, Angel falls through a mirror sculpture into a bronze-age world, and meets Winter, a boy with the same names as the fantasy boy in her virtual reality game. Eventually, disease hits his village and they escape back into Angel's world where her mother tries to make her a celebrity. Angel and Winter run back through the sculpture.
This first book rather over-eggs the pudding: the world is so horrible, Angel's parents so uncaring. This is a teen view of the world but it doesn't offer much solution, In some ways it's a lot like N.Roy Clifton's The City Beyond the Gates in that although Cooper makes some sardonic comments about it being a good thing Angel doesn't ask the villagers what the cute bunnies are for, there is a lot of wistfulness for a simpler way of life.
The second book is much more interesting. When Angel and Winter go through the sculpture they find Winter's world isn't quite as they remember it. They end up running again, and this time they end up in a not-quite-Angel world where there is an Angel but it's the daughter her mother would actually have liked (pliant, not too bright). They try again and end up ricocheting between different worlds until rescued by Pye, who they had thought was threatening them but is actually the scientist who made the sculpture. He asks to take them on as apprentices. Winter agrees, Angel declines. She goes back to her own world, can't cope with it, and is rescued by her own ingenuity (she builds the sculpture anew in virtual reality) and by Winter and Pye.
The book is about leaving home and growing up, about refusing the socialisation cues. Although Winter is clearly a love interest, it isn't forced on the reader (ie I could ignore it). And there is a very cute electronic cat who also makes its own little feline decisions by the end of the book. What more could you ask?