Hi C.,
I totally remember this time...my little one is 2 1/2. My son had irregular sleep times during the day as well. And around 3 months his night time sleep was similar to your daughter's.
What I did was this. When he woke up, I began counting down two hours. And I would put him down every two hours and I didn't care if his sleep was 30 min or longer. When he woke up, I began the two hour count down. And I made sure his room was like night time: sound machine and black out window treatments. When I began putting him down as such he became more agreeable (not cranky). Then what I also did was NOT put him down after 4:30 pm. And if he was still sleeping close to 4:30/5:00 pm I would casually wake him up (open his door, talk louder when in another room, etc.)
And then I began his night time routine around 6:45 pm which allowed me to finally place him down for his night sleep around 7:30. And to this day, we start his routine at 7:30 pm and he is down by 7:50 and I am off the clock.
He wakes every morning around 8/8:30 sometimes he'll hit 9:00 am. He has his two hour nap at 2:00 pm every day. I can't beat it. Good luck to you. And one more thing that saved me was being flexible. Even though I thought I had a schedule it was actually a guideline. Best to you.
C.