If I change the word "facing" in the context below to "in the wake of". Do they still have the same meaning?

Question

The word 'facing' i refer here is the capitalized one.

Context:
In FACING the regional autonomy era, regionalization and globalization, the big problem encountered by the country is how to produce independent and tough children in facing a very tight competition with other nations in the third millenium.

Answer 1

I think Selket meant to say that FACING points to the future and IN THE WAKE OF to the past.

With "facing" the regional autonomy era is coming up; with "in the wake of" it has already started and is already producing effects.

If this is your own sentence and you've noticed the problem with having two "in facings" in one sentence, I can recommend eliminating the second one, because it is in no way clear who or what is doing the facing. (Facing is a participle--it's acting as a noun but it remains a verb--and therefore it needs a subject, whether stated or implied.)
In your first use of "facing" the subject is "the big problem". Of course it should be "the country"--this can be neatly resolved by eliminating the passive voice in "the big problem encountered by the country", replacing it with "the country encounters its biggest problem, that of how to produce..."

If you don't want a subject for facing and you do want the "look to the future" aspect, you could use "in the face of".

Answer 2

nope, they mean opposites.

In FACING... the big problem ... is <- this means the problem AFTER the regional autonomy era.

In THE WAKE OF ... <- this is referring to the big problem AFTER the regional autonomy era.