I don't understand why the inversion of the phrases is incorrect, i.e. "If you help me, I'll help you".
The Klingon can be phrased as either, qaQaH choQaHchugh or as choQaHchugh qaQaH. When deciding in which order to present the two parts many times you will just randomly pick an order and in a case like that the order of an English translation wouldn't really matter either.
However, there are times where you have specifically chosen an order to create some effect. When someone asks you to help them, you might say, "I'll help you... if you help me." Or perhaps you are trying to get someone's assistance by making them an offer, "If you help me, then I will help you." Sometimes the order matters.
Since both English and Klingon can change the order in similar ways for similar effects, the order should be maintained in the translation and qaQaH choQaHchugh should not be thought of as exactly the same thing as choQaHchugh qaQaH.
For exactly this reason, many of the sentences in this course have exchangable parts and we require you to keep them in the same order in both the English and the Klingon.
Can either of you say anything to clarify that conjoined phrases like this have a different rule about order than the rules about object subject word order? When a comma is included in the Klingon, it is clear that the first part comes first and the second part comes second. In this case, there is no comma.
The comma is completely optional and is generally used for clarification. We have decided to use the comma consistently for direct address to keep it clear for beginners, but outside of this course you will seldom see it done that way and the prefix will usually be your best indication of whether a noun is direct address or whether it is an argument of the verb.
Similarly for sentences like this. When the comma is included, it is for purposes of making it easier for beginners to parse or for clarification when there are two ways to interpret a bit of grammar. Outside of this course you are probably less likely to encounter such commas. And even in this course we don't consistently use or not use the comma to mean anything with regard to such subordinate clauses.
The basic rule is, keep the same order in both the English and the Klingon unless there is a grammatically rule for changing something.
For instance time stamps such as wa'leS "tomorrow" must go at the beginning of a klingons sentence and usually sound most natural at the end of an English sentence. Thus you will likely see an English time stamp at the end of sentence matched with a Klingon time stamp at the beginning of the sentence. In that case, it is grammatically necessary to put the time stamp in a different place in the Klingon sentence.
However, with the subordinate clauses created by many of the Type 9 suffixes such as -chugh "if", -DI' "when", -taHvIS "while", etc., in both English and Klingon you have the choice of presenting either the main clause first or the subordinate clauses first with almost identical subtle rhetorical effect. Thus, whether there is a comma or not, the clauses should be kept in the same order with either the main clause or the subordinate clause appearing first in both languages.
The only exception is -meH "for the purpose of" which must always appear before the main verb in Klingon, but can appear in either order in English (though it's not really a subordinate clause anyway).