What is the order for 雖然 and 當…的時候 when used in the same sentence？ Example sentence: 雖然當我們在一起的時候有時候我不常常說話、而且我可能正顏厲色、我要讓妳知道我很開心。

Intended meaning: Although when we are together sometimes I don't talk very much, and also my face may be solemn, I want to let you know I am happy.

Is there a specific order? My second guess would be:

當我們在一起的時候雖然有時候我不常常說話、而且我可能正顏厲色、我要讓妳知道我很開心。
Is there a specific order for 雖然 and 當...的時候? 

No, I do not think there is a specific order for 雖然 and 當...的時候

A way to see the reason is that , you can insert commas in the sentence and see that 當...的時候 is a adverb clause, and 雖然... is a conjunction word. 

(1) 雖然, 當我們在一起的時候, 有時候我不常常說話, 而且我可能正顏厲色, 我要讓妳知道我很開心。

(2) 當我們在一起的時候, 雖然(,)有時候我不常常說話, 而且我可能正顏厲色, 我要讓妳知道我很開心。

(3) 當我們在一起的時候, 有時候我不常常說話, 而且我可能正顏厲色。 雖然這樣, 我要讓妳知道我很開心。

雖然這樣 is a way to connect a subordinate clause in Chinese.

There is a order for 雖然...但是...

雖然媽媽總是批評你，但是她還是很愛你的。