The book I am looking for is one I read in the mid to late 70’s about a girl (and I think her sister) perhaps named Lydia. Their parents are part of a witch/warlock community that are in some kind of other dimension. Somehow they get abandoned by their parents and go off searching in the other dimension. The whole time they are carrying a mouse in a cage that ends up being their father (complicated family dynamic!). The book is printed with occasional drawings of their adventures including one where they are forced to clean up the kitchen of some captor. I think they end up freeing a dragon whose collar is unlocked by a key that the mouse had – or something like that. I have spent years googling and haven’t been able to turn up anything. Thanks!