It is grammatically correct, and I am sure that any native English speaker would understand, but you are correct in saying that it does not sound (quite) right. I think English speakers would say "We are in serious difficulty" or, even more likely, "We are having serious difficulties" Alternatively, if there were any doubt "Seriously, we are in difficulty".
"We are seriously in difficulty (or, trouble)." and "We are in serious difficulty (or, trouble)." have two different meanings. In the first, I am really serious about the fact that we are in trouble. In the second, I am stating a fact the the trouble we are in is, itself, very serious (has great consequences). Since this is lesson on adverbs, it would seem that only the first of the above translations makes sense.