It is a complex-compound sentence. There is only one main clause, but there are multiple subordinate clauses that are coordinated on their level:
Along with every other devoted Aussie trackydack dagger, I beg the federal government to
This is your core of your main clause. What follows are the subclauses:
- ban these abhorrent, foreign "cuffs"
- and bring back the loose, flaccid Aussie leg-hole we know and love.
These two subclauses are linked by and, so they are coordinated, but only on their level and not on the level of the main clause. Within the last subclause you have once again two coordinated clauses:
- the loose, flaccid Aussie leg-hole we know
- and love.
I hope the sentence structure is now clear. Looking from the main clause, this sentence is complex, since there are no coordinated main clauses (there only is one main clause). I'm not sure if you need to look at the levels of the subclauses as well, but I've explained that anyway. Since the two first subclauses are coordinated, they are compound, but because they are dependent on the main clause. This is why we call this a complex-compound sentence. Note that this is NOT a compound sentence. You always look at the main clause first. Is there only one? Then it cannot be a compound sentence. If there is more than one main clause then they are linked by coordinating conjunctions (such as a comma, and, semicolon).
The last two subclauses, that are found within one of the two coordinated subclauses, are not taken into account when determining the type of sentence. Only the first two levels are normally looked at.
You obviously know the difference between a complex sentence and a compound sentence. Now you've seen what a complex-compound sentence is and as you might guess, there also exists the type of compound-complex sentences. They consist of multiple main clauses where at least one of these main clauses has a dependent subclause.