You being a U.S. citizen has nothing to do with it, it's not you that is applying.
You have to look at it from another point of view.
All of her immediate family are in the U.S., you said yourself that the reason she isn't there also is because she was over 18 at the time.
I don't know why you mention asylum seekers, people use tourist visas all the time to "visit" family and forget to return home. I don't know the statistics but I imagine there are far more cases of tourists abusing their visas than there are asylum cases.
No one is saying that's what you're doing but that's the way the consular officers look at it. They don't know your stepdaughter and have to guess her intentions based on what is in front of them.
That all sounds quite negative but you shouldn't let that stop you trying.
People get approved all the time but it's always best to remember that it's not guaranteed and there's very little you can do to help other than give her advice to think more about what her reasons are for returning to Honduras and less about her reasons to want to be in the U.S.
They don't care why people want to visit, they only care that they'll go home again afterwards.