Complex sentence: Seeing the battle between the Joule Team and the terrorists on Junius Seven, they misinterpret it as the Joule Team was helping the terrorists cause Junius Seven to crash into Earth and attack both sides indiscriminately, hindering ZAFT's efforts to break the colony in half.
Split into simpler sentences: Seeing the battle between the Joule Team and the terrorists on Junius Seven, they misinterpreted it as the Joule Team was helping the terrorists cause Junius Seven to crash into Earth. The three than proceeded to attack both sides indiscriminately, hindering ZAFT's efforts to break the colony in half.