Exiting Mao's home, turn left and walk straight on to Mao Zedong Sq where, on your left, you'll see the entrance to this museum. It portrays Mao's life through paintings and old photos and has decent English captions.
Exiting from the back of the museum, you'll see the Relic Hall of Mao Zedong in front of you. This more modern museum includes everyday artefacts used by Mao, clothing he wore, plus more photos from his life, and also has good English captions. Turn left as you exit here to get back to Mao Zedong Square.