It sounds like your dd has programed herself to wake early and just needs your help to reprogram herself to wake later. It also sounds like she is overtired, staying awake from 2pm to 8 pm might be way too long for her to handle, then she can't settle and stay settled. I would try 2 things. First, don't get her up when she wakes at 4am. Decide what time would be ok for her to wake at, say 6am, then keep her in bed until 6am. Don't go to her until she cries, then use whaterver sleep training method you are using to keep her in her bed until time to get up at 6am. My dd (now 15mo) has had several periods where she wakes at 4am or 4:30 and I found that if i let her alone, she would play by herself, sometimes for an hour, then go back to sleep on her own and sleep until 7am. Even now, like this morning, she woke at 5:37am and I let her alone until 6am, she played happily with her blanket until i got her up.
The second thing I would do is shorten the time between naps so that she is not awake for more than 3.5hours, so that means she is asleep after 3.5 hours, if she wakes at 5:10 then she should be asleep no later than 8:40am. My dd was asleep at 8:45 this morning. I would also let her sleep as long as she wants so that she is napping for 3 to 3.5hours a day. That's really not too much daytime sleep for a dd her age. I would also make bedtime earlier, in bed at 7pm if needed. My dd usually wakes from her pm nap around 3:30 or 4pm and was having a hard settling for her last nursing at 8pm, it would take her 40 min to settle and nurse so she wasn't getting into bed until after 9pm. then I started bathtime earlier at 7 and nursing at 7:30pm and now she is in bed and sleep at 8pm and sleeps til 5:30 or 6am. I realized that I was keeping my dd up too long after her pm nap, staying up for 4 hours after her pm nap was just too long and she couldn't settle at bedtime, and so your dd may also need an earlier bath and bedtime. If she wakes at 2pm, she may need to be in bed at 6pm until you can get her am wakes later so that she wakes later from her pm nap.
Remember this will not last forever, it may last a long time but it won't be forever. You are doing everything you can to help her and that makes you a great mom. good luck.