How long for grandparents to get custody of a child?

Hi,

My novel situation is such: My MC is a minor (16) who moved from the US abroad with her mother several years prior. The move was after divorce and with the father's permission. The place they moved to encourages arranged marriages, and the MC's mother and their community is trying to push her into one. The MC asks her grandparents, who are in the US, to look into getting custody of her and pulling her out of the situation. My question is, primarily, how long of a process would that likely be? Would it make a difference if the MC said "they're talking about marrying me off within a year"?

In the book, I have the MC taking initiative to run away and get back to the US on her own, but it's a very risky situation, and I don't want people to be going, "If she'd only told her grandparents what was going on, they'd have her out in a few weeks." For example.

I would appreciate anyone pointing me to the expert who would be able to answer this, if no one here actually knows.

Thank you all for your responses. Mentioning the embassy was helpful, Fruitbat. I should incorporate that into my novel.

I'm really trying to paint my MC into a corner, good and challenging. The place she and her mother live is an experimental community on a tiny island. I haven't figured out if/how it would be under the jurisdiction of another country, and which one, but the island is so small that it, like some other Carribbean islands, wouldn't have an official embassy location or representative. So no direct help there. She would have to get transportation to the embassy in Bermuda, probably. And her government is really stingy about who can travel and why.

Also, she wants to go back to the US for a visit, but her mom won't take her, or give her permission to go, due to strained relations with the grandparents.

ALSO, she has lost contact with her father, because he moved around in recent years and didn't try to stay in touch, so she can't apply to him for help. (I'm wondering now, though, if she might have contact info for his parents/family, and reach out to them.)