Naptime advice

ArcticFox

I desperately need naptime advice.  I've been getting a lot of criticism, and I rarely get help with the kids, so I need some constructive help.

DD is 2 years+2 months, her schedule is:

7:30-8:30 - wakes up

2-4pm - naptime

10pm - bedtime

However, she loves to sleep in late.  I try to have her up by 8 at the latest.  She also generally likes to sleep past 4pm, but if she does, then she goes to bed at like 10:40 (even if she only sleeps til 4:10).  If I wake her before 4pm, she is MISERABLE and cranky.  

Also, if I get her up a lot earlier - or like when we had the time change, she was melting down at noon, and I need to be at preschool picking up my 4.5 year old, and then it means I can't ever go to lunch or even make it through lunch for that matter.

Any suggestions?  The day after Xmas, I accidentally overslept with her til 9am, so then I got rid of her nap that day because I certainly wasn't going to put her down at 3/3:30pm.  She slept about 8:30pm-8am, but she was cranky in the evening from missing her nap.

And I have tried everything to get her to take her nap earlier - lullaby, white noise, lavender, milk, rocking her to sleep.  So I'd love any help! 

ETA - I also do a big routine for bedtime - snack, bath, stories, and then everything I do for her nap.  I'm desperate to get her to bed earlier, I'm about to lose my mind over her late bedtime.