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。
From your English I would get this:
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.
尽管有时候，我们在一起时，我不说话而且看起来很严肃，但是你必须知道，我心里很高兴跟你在一起
