Sorry for your plight Skyfall.
 
I have a couple of friends who have been through very similar. One being the 'other' father who cared for and loved his partners daughter like she was his own. Then years later the real father turns up. My mate wanted to kill him for not being man enough to try and be a part of his real daughters life and for giving up on her.
But i tried to get him to see it from the other side. His ex was a real b*tch, i mean evil as hell. Who knows what lies she spun to the real father, and her daughter for that matter.
Now... 4 years later, regardless of your reasons, you may possibly enter this little girl's life and turn it upside down.
She won't fully understand what a 'daddy' is, her mum could have told her all sorts. The norm for her is 'mummy and me', unless there is another guy on the scene, in which case he may be 'daddy'. If that is the case you have no chance i'm afraid. Oh the law may fend for you, but thats the law, it doesn't deal in human emotion and turmoil. You will be torn even more because you'll likely never have the relationship with her that you desire and you are so far away. Her mum will never let you be the father you truly want to be. Sure, she may take your money, but it doesn't buy love mate. If your ex is single then 'mummy' is likely your daughters only role model and she would trust implicitly. You could be about to shake the very foundations of that. Its not fair, but what's more important, you making contact and possibly screwing her life up or her happiness?
When this happened to my best friend, i asked him, almost pleased with him to try and cut loose his 'daughter' for his own sanity. At 14 she now only acknowledges him when she wants money...same goes for her real dad. She's the spit of her mother (b*tch).
 
My boss also separated from his wife. She had his daughters aged 6 and 8. They are now 15 and 17 but in that time since, their mother has poisined them against him. I've seen emails of them telling him to 'F' off and die! He was devastated for years.
Now at the age they are, they are questioning their's mothers wisdom and stories.
But damage has been done. If he dies, they become millionairesses, i wonder if the superficial characteristics of the mother has passed on to the daughters. 

 and thats why they are only now having contact (via FB)
 
I truly hope you find peace mate, but think hard about what you desire and what could happen. It may just mess this little girl up (....even more?)