1.那次旅行的目的是探亲跟去玩
The purpose of that trip was to visit relatives and have some fun.
2.语法错误,正确句子应该是：
The most embarrassing moment she had happened in China.
happen是一个不及物动词,因此不能说was happened
分析：句中she had是一个定语从句,修饰前面的moment
moment为句子的主语,谓语是happened
翻译：她最难堪的时刻发生在中国.