I can see both of Rory's parents in her as well as both her grandparents. I think Rory has always been a bridge between Lorelai and Emily. She kind of puts herself there to settle conflict but also Rory gave Lorelai the strength to leave but also the reason to return more regularly.

Rory is her own person, She isn't this beautiful free spirit that Lorelai is in that she is more reserved and grounded. She's much more a natural people pleaser (in the best way in that she wants people happy not that she wants to gain something from the person). She's also doesn't instinctually need to feel independent. She relies on the people in her life and not really reluctantly. She also relies on list and plans and structure much more so than Lorelai. She does do impulsive things though but it's more about stress or emotion than a personality trait. None of the Gilmores learned how to cope with stress and emotions healthy.