And that 的用法要根据上下文判断, 经常和前面的句子有关系，有时用来表示强调或加强语气。我在网上搜索到该句子的部分上下文。它出自Nathaniel Hawthorne  的名著 The Scarlet Letter《红字》的简写本。All these things led people to believe that Pearl was not only alive but also married and happy. And that she did not forget her mother and always kept her home in England open for her, if Hester should ever want it.

    根据上文，and that 引导的从句实际上与前句believe that 后的宾语从句并列的，作者把这个从句独立成句用于强调，在这里可以译为“而且”，这也是and that 常见的用法。而且Nathaniel Hawthorne喜欢使用and that 引导句子，仅在《红字》一书中就出现了几十次。