Don,
There are ways round this, but it does mean going to court, if the Ex husband is of the stubborn type (which most are) A lot depends on two factors, the first is, if he has been supporting his daughter financially, the other on if he has remarried.
If no financial support has been given, your on a very good start, If he has remarried, then it is unlikely that his new wife would be willing to support the daughter by inviting her to live with them. The fact that it is a daughter, is also in your ladies favour. The Chinese men will not normally put up as much fight for a daughter than for a son. All to do with retaining Family name and the like.... So, if these two conditions apply to your ladies Ex husband, you have a good fighting chance of winning the full custody of her daughter....
So, ......Initially do as Maxx suggested, be sure of your feelings for each other first and foremost. If everything works out well on your visit, and you decide that Marriage is what you both want, then start the full custody fight. You may even find, that he backs down, when he knows that she has filed a suite in the court, it might even be his new wife, that tells him to drop his objections, because this is going to cost him money also.
If this was a boy, we were talking about here, i would probably tell you to drop any thought of you and your lady wining your day in court. It has been known, but very rarely.....
David.....