that引导非限制性关系从句和引导同位语从句的疑问？

She had had the idea of giving it a certain daintiness, and she made much use of blue and red inks; she bound the copy in coarse paper, that(1) looked vaguely like watered silk, in various pale colours; and she had acquired a reputation for neatness and accuracy. She was making money. But she could not get over the idea that(2) to earn her living was somewhat undignified, and she was inclined to remind you that she was a lady by birth.

请教老师：

句中我标注的that(1)和tha(2):

that(1)是引导非限制性关系从句，这里为什么用了that，而没有使用which呢？

that(2)在这里是引导同位语从句吧？问题是，后面为什么是to earn her living, 而不是owning her living 呢？