Complex sentence: When Andujar decided to get more involved in politics, she joined the Republican Party, which was rebuilding in Texas after weakness in the early decades of the 20th century following state disenfranchisement of minorities.
Split into simpler sentences: When Andujar decided to get more involved in politics, she joined the Republican Party. It had been rebuilding in Texas after weakness in the early decades of the 20th century following state disenfranchisement of minorities.