Complex sentence: Stevens was uneasy about having a delegate support an issue she felt drew upon differences between men and women, but she needed Vergara and MEMCh's support for the Equal Rights Treaty, which was facing strong opposition from the US State Department.
Split into simpler sentences: Stevens was uneasy about having a delegate support an issue she felt drew upon differences between men and women. But, she needed Vergara and MEMCh's support for the Equal Rights Treaty, which was facing strong opposition from the US State Department.