This is where the rubber hits the road in your family life going forward. If he misses the trip, if he fails to be anything but fully supportive it is her he is harming at a point in time when he should be accepting, and praising, and making her feel worthy for all parts of herself. That's his job as her father.
At 13, she is in the Ophelia time, a critically important time for adolescent girls as it is the time when they form their personality, or fail to do so. If they fail, it can result in slowly losing their identity and becoming submissive. His top down ultimatum is repressive at a point in time when it should be expansive. Africa is a perfect choice for her right now for her developing personality. It will not cause her to love him any less, but not letting her go will, and it will fester over time.
He is throwing a wedge between his daughter and himself, a wedge that will continue to grow as she grows older. He is actively threatening her full existence as a dual race person, but he does not, or refuses, to see it. That's a huge problem with regard to how he treats his own child.
The ancestral root heritage of her father is all around her. Yours is not. Whatever he thinks he's doing, what he's actually doing is calling her out as "less than" white. He's doing it to you, too, psychologically and systemically. It's a beat down. The message is half of her is not as good as the other half. And all of you, well, you get the idea.
He needs to get on the plane, get on the train, be 100,000% supportive, pleasant and loving. Anything less is harmful to her and truly potentially harmful to her long term.