"the child's mother has never been in her life since she was born, so she lived with her grandparents. "
I have a feeling this is where the problem started. Why wasn't she living with her dad? You're very well intended, but the deck was stacked against you right from the get go. Her mom bailed on her, her dad did the same for awhile, and now she's living with "evil stepmom" having to compete with a half sib and another on the way.
Again, none of this is on you, but too many kids today are born into unstable situations, and this is always challenging. Kids need stability almost as much as love. Now ,on top of everything else, she's living in a strange country.
You aren't going to fix this (at least for a long while). However, your husband can undo a lot of damage. Does he ever have alone time with her, or take her on special excursions just for her? On the surface, it might sound like a bad way to build a "family", but it isn't. It wouldn't come at the expense of family outings and you can do something with your child while this goes on. She just needs to know that the most important person to her - her dad - has her back. Once she feels secure in this, she'll realize you aren't a threat to her. But he has to be the driving force.