Bastila's Mother Side Quest - Tatooine (Kotor 1)
In Kotor 1 almost all of your Companions get their own "Companion Quest" which involves a story line unique to them. To trigger these quests you will need to talk with your party members and listen to their stories for new Journal entries. Sometimes you can just talk to them on the Ebon Hawk or if you have them with you in the world to advance their personal plot, other times you'll need specific events.
Bastila's Companion Quest involves her mother who is found on Tatooine in the Cantina. You can start this quest at any point after hearing Bastila talk about her mother in dialogue, you'll just need to wait until you're approached with Bastila in your party at one of the event locations.
After learning about Bastila's mother being on Tatooine you'll also be approached in the town of Anchorhead by Maana Demknot. He'll tell your party that Bastila's mother is indeed in the Cantina and is being absolutely intolerable.
Speak with Bastila's mother inside the Cantina and you'll finally begin the quest. There are no opportunities for Light Side or Dark Side Points during any of the conversations for this quest so answer whatever you wish. After some dialogue you'll be tasked with finding a holocron in the Krayt Dragon cave on Tatooine.
If you've already completed the story for this planet then you'll probably already know where this is, right next to the Star Map. For those of you who haven't completed the story yet, check my Tatooine Walkthrough for guidance on exactly what you'll need to do.
You will find the Holocron we need inside of a Tattered Equipment Pack at the back of the cave (pictured below). Grab it and return to Helena in the Anchorhead Cantina for the final part of the quest. Note: You can talk with Bastila about the Holocron after you find it if you put her in your party.
There will be no opportunities for Light Side or Dark Side Points in your final conversation with Bastila's mother. However, you will be able to encourage or discourage Bastila from reconciling with her mom. It's up to you which of the two routes you choose, the reward will be 250xp regardless.