Is this sentence correct? "She is trained in the teaching of the English Language." Is it correct to use " the" before " English Language"?
Both uses of the word the are a bit awkward in this sentence.
A cleaner, simpler, more active sentence would be:
"She is trained to teach English."
It would be OK to have "the" before "English Language" in this sentence:
"Her teacher training includes the English Language."
"She is trained to teach the English Language."
In both of these cases, the word "the" goes along with the structure "X Language", to indicate that it is this particular language that is being taught, out of all possible languages.
The clause "...trained in the teaching of..." is cumbersome and not informative. You are substituting a noun phrase "..the teaching of..." for an infinitive verb "...to teach...", which takes away from what you are trying to say.
If, instead, the subject was an academic researcher in the field of Education, then we might say that "She has studied the teaching of the English Language.", which would mean that she has studied, observed, or has knowledge of how other people teach English, and what makes them effective or not. This researcher may or may not be a good English teacher herself.