To me, the only satisfactory solution with "poorly" is to place it at the end.
"E understands A culinary habits poorly."
Even so, this is not a very idiomatic sentence.
Another solution is "E does not understand A culinary habits well".
This is more idiomatic.
Another good solution has already been suggested.
"E has a poor understanding of A culinary habits".
I prefer this one above all the others proposed so far, and I would
ignore any "rules" about avoiding the verb "have" in this case.
CJ