It's all very well you wanting to take it on and fight all the way, but what does your daughter think - has she been give an chance to express a view since it is her neck on the line if your fight goes pear-shaped?
Smoking is a filty habit and you raise another interesting question about the size of the fine, it is a lot to your daughter who is presumably skint, yet there will be a lot of others to whom £50 is what they would spend on a drink and couldn't give a toss. So do you then fine people according to ability to pay?
There is also the question of whether chucking rubbish should be an offence or not, Are you arguing that it should not be in general, or just in your daughter's case? what constitutes rubbish? a single item or only lorry loads?
An interesting question - it raises all sorts of issues!
You are obviously annoyed by the fact that she got caught and not by a policeman. So