L.G.
A.,
I can certainly relate to your situation. My oldest daughter had the same sleeping routine. My youngest daughter slept much better than her and still does today. Some sleep patterns are just individual rhytms and the best thing you can do for them is make small adjustments over time with a goal of meeting somewhere between what works for her and what works for you.
That being said, there are some things you can look for and some things you can do to help make those small adjustments easier.
Keep a food chart and notice if certain foods make it less easy for your daugher to get to sleep and stay asleep. Create a bedtime ritual. It may need to be an hour-long ritual to help her wind down and get ready to sleep.
Whatever you choose, make sure it is as respectful to your daughter as possible. One day you may be grateful that she is a night-owl (like when someone is waiting up for your younger child to come home as a teenager)...
By respecting your dughter and her natural rhytms you are also modeling the respect you want from her.
One thing that worked for me when my daughters were 3 years old and 6 months old respectively, was to make my older daughter's room completely safe, and then to let her know that after a certain time, she could be awake (in her room) but she had to respect my need to sleep by staying in her room and playing quietly. I put a latch high-up in the outside and kitchen doors, so she could not get out of the house or into the kitchen....
I knew sleeping or not, she was safe.
Hope this helps,
L. G