In morality bites Prue never got over the loss of Andy. If we look at Prue between seasons 2-3, she never really found another love, no stable boyfriend. I believe in this timeline she just gave up. Focused on her career, figured she'd let the Halliwell line continue through Piper and Phoebe. Maybe thought that after losing her soulmate there was no one else for her.

And seeing as how she was the president of Bucklands, and had opened offices in several other countries, she probably spent most of her time in those countries setting up other offices.

Piper was focusing on her marriage and children.

Phoebe never met Cole not did they take on the source since they weren't such a big threat anymore. When her friend was murdered her empathy grew into rage from the trail, the witnesses and murderer until she took justice into her own hands.

I think in this timeline the sisters grew apart, there bond weakened. Each sister focusing on a different path. Then when Phoebe was arrested that probably bought Prue and Piper back together in an effort to save their sister.