how old is your daughter? ,
i'm a bit surprised the judge went in your favour at the appeal but i dont know the facts or i'm no expert , but it seems you've not lived with your daughter for at least 2yrs ?? and you would need to prove you have 'sole responsibilty' thats not the same as 'sole custody' and i think this might be a problem as she has contact with her father ( you said you used her fathers address for her)
what visa do you have FLR, ILR or ??