Our daddy with tears running down his face, promising God his life for the safe return of his girls.

以上句子不完整。建议改为：

Our daddy, with tears running down his face, is promising God his life for the safe return of his girls.

【翻译】我们的爸爸，热泪从脸庞流下，向上帝承诺，愿献出生命换回女儿们的安全归来。

【分析】

1. promise sb. sth. ：向某人承诺某事。promise God his life，意为“向上帝承诺献出生命”。

2. for the safe return of his girls：为他女儿们的安全归来。

3. with tears running down his face：with复合结构，作方式状语，修饰is promising。