The schools do, indeed, all have different criteria for admission. I am not familiar with all the criteria for every secondary school in Trafford, but I am sure that the vast majority, if not all, use distance to determine at least part of their intake and North Wales would be way too far away to get a place. The Trafford schools are all incredibly popular due to their great results nationally.
If you look at the grammar schools in particular then you have one potential option which is Sale Grammar. It's a co-ed grammar and it admits a large part of its intake from its catchment area (where, to qualify, kids just need to pass the exam). If there are spare places left after it has allocated to the catchment kids then it allocates its remaining places according to high score. So even if you live in Timbuktu, let alone North Wales, if you score extremely highly, you would have more chance of getting a place than someone who lives in Chester but only got the passmark.
(For the sake of completeness, and any other interested person reading this thread, I must also mention Altrincham Grammar for Boys which allocates on exactly the same basis as Sale, although its catchment is much smaller. This isn't helpful to you, though, since your daughter would need a quick sex change as well as a high score
Have you looked at the Wirral Grammars?