Complex sentence: In 2004, shortly after it was opened, Estonian Government, possibly due to pressure from the EU and the USA as well as other international organisations, opposed unveiling of the monument, and ultimately ordered it to be removed.
Split into simpler sentences: In 2004, shortly after it was opened, the monument was removed because of the Estonian government opposed the opening. The Estonian Government, possibly due to pressure from the EU and the USA, ordered the monument to be removed.