Yanqing was driven to Liangshan because he was in trouble with his master Lu Junyi and had to take action to protect himself and his master.
The reason why San Niang was forced to go to Liangshan was that she was captured by Song Jiang, and her family came down and she had to join the partnership.
Sun Erniang was driven to revolt because she had to kill people to make meat buns in order to avoid being chased.
Gu Dasao was forced to go to Liangshan because she was desperate and robbed the prison, so she couldn't continue to open a hotel to make a living, so she had to go to Water Margin.