We can say both 静かなかわいい子 and かわいい静かな子. かわいい and 静かな are attributive form and they modify 子(a noun). You can also say かわいく静かな子 and 静かでかわいい子 and the former adjective is 連用形(conjunctive form) and modify the adjective after it. They are all the same meaning.
理想の店員の態度 can mean two ways as you said but I feel it indicates "the ideal attitude of a store clerk." than the another. If you want to make sure the meaning of "the attitude of an ideal store clerk", it would be "理想の店員がする(行う)態度.
最初の日本の専門家 usually means “the first specialists in/of Japan” because 最初の日本 rarely means "early Japan" but 初期の日本 means it. In addition, even if you change the order of 日本の and 最初の, the meaning is the same, but you can't change the order of 日本の and 家の in 日本の家の専門家 because 家の日本 don't make sense. That is to say, when you change the order, there are the cases that the meaning didn't change like 初期の日本, there are the cases that it doesn't make sense like 日本の家 and there are the cases that the meaning changes like 英語の先生.
For example, the order of the noun can't be changed in 私の家の庭の木の下の穴(the hole under the tree in the garden of my house) because the each noun modifies a immediate noun after it.
We can say both 天来の美しい歌 and 美しい天来の歌 as the same meaning but 天来 isn't common.