Sleeping

My daughter is 2 and she still is having trouble sleeping through the night. We adjusted her bedtime for an hour later than usual, cut her nap down to an 1.5hr, give her a snack before bed. She wakes up anywhere from 2 am to 5 am (depends on the night and how long she stays up varies). She also does NOT go to sleep without playing music anymore. We did it one night because she was sick and the song was the only way to get her to calm down and she fell asleep in my arms with it playing. Now she won’t sleep without music playing ALL NIGHT. If I turn it off she wakes up 10-15 minutes later. I’m so exhausted. She doesn’t get milk/bottle anymore. She has a very strict schedule with everything and doesn’t do well with change. When we changed bedtime from 7:30pm to 8:30pm she was miserable for two weeks until she got used to it. When she gets up in the middle of the night SOMETIMES she cries and needs help going back to sleep but other times she’ll just play with her cow and dog stuffies and eventually sleep whenever she’s done. Sometimes she’ll sing at the top of her lungs or kick her crib until she sleeps. I don’t know if she’s not getting enough activity in before bed but we do a huge playtime an hour to hour an a half before bedtime. I’m basically just looking for some help 😭 her pediatrician told us that the 8:30 bedtime would help and it hasn’t. Any advice? We also don’t do screen time 2 to 2.5 hours before bed. Whenever she does have screen time it’s all incredibly low stimulation and she’s actively playing and the tv is just kinda in the background. I have a 5yr old sister who she runs and plays with ALL day long so I can’t imagine that she’s not getting enough activity during the day. She also holds her pee all night so it’s not wet diapers that are waking her. We tried having her pee in the middle of night but she doesn’t go. We started offering a small cup of water overnight for her incase she was thirsty.