10.5 year old girl with persistent insomnia

My daughter is 10.5 years old. She is in puberty, and at her yearly pediatrician appointment in June, the doctor said she will likely start her menstrual cycle before her 11th birthday in mid-December.

A few things about my daughter: She is not a typical 10-yr. old. I think she just missed the autism spectrum on the Aspergers side. (I am 99% certain my father has undiagnosed Aspergers.) It could just be sensory processing disorder, but when she was younger, in kindergarten, she would "stim" at times (hand flapping, a weird repetitive neck motion), especially when I told her it was time to do something she didn't want to do like get ready for bed. She seems to have outgrown that, but it was there for awhile. She also had total and complete meltdowns at school through the 3rd grade. Pretty much in every sensory area, she has some issue. However, she is also highly intelligent. She scored 100% on the math state standardized test in 3rd grade & 4th grade too (STAAR) and 98% on reading both years. She's going into the 5tth grade, but all the computer reading programs put her lexile reading level above 12th grade. She figured out multiplication on her own. She can write numbers in binary and bases other than base 10, even bases like hexadecimal. She has a big interest in writing, computer coding, computer illustration. She is introverted, and her social and some of her mobile skills were/are delayed (didn't jump until 3.5 years old, still takes the stairs downwards in a weird way).

So...she is not the average child even though I realize all children are unique and have their own set of parenting challenges.

She has never been an easier sleeper (colic, few naps as a baby & toddler, hates going to bed). Near the end of the school year last year (4th grade), she started to have insomnia off and on. I finally got to where I told her to stop waking me with it, set a timer for 30-45 minutes and read or play, and when the timer goes off, try to sleep again, and if she still can't after 30 minutes and just feels she is awake, to get up.

I struggled with awful insomnia my whole life, but when I was a kid, I just stayed in bed with it though I'm sure once I had my own room (shared with a sister until around 8th grade), it would have been fine for me to read; my mom wouldn't have cared.

My daughter gets panicky with her insomnia. Like if she will have school that day, and she can't sleep and it's 4 AM, she will wake me up all anxious about it. I had to cancel a playdate with one of her cousins just last week because she was panicky about getting up in time (around 7 AM), and it was already past 3 AM.

All these panicky situations wake me up at night and despite the cocktail of meds I'm on, I'm a light sleeper. So even when she's not panicky, I'll sometimes hear her awake or using the restroom, and it wakes me. Her bedroom is close to ours, and our house is not that big, around 1400 sq. ft.
Once I wake up after going to bed & fall asleep for the night, I can't fall back to sleep if woken up in the middle of the night until maybe late morning or the afternoon. When I don't get enough sleep (besides the issue of it contributing to hypomania), I tend to be a grouch.

I just don't know what to do with her. Any ideas? The pediatrician said to give her melatonin at night, but my husband feels strongly that would be like drugging her, and he doesn't want to do that. And what do I do? Continue to wake her a 7:30 or 8 AM even if I know she didn't fall asleep until 5 AM or just let her sleep? Today, she slept until nearly noon, but she was still up at 3 AM. I think she spends a lot of her time awake reading because if I check her iPad batteries in the morning, they will usually be 95% or higher, and she never charges her iPad until the battery gets down to around 10%. And I know she is not watching TV though I wouldn't put it past her to play on my or my husband's computer.

Worse, my husband is lax about her sleep habits. He is a teacher, and I'm a homemaker. I'm the one who hears the alarm and usually wakes everyone for the day when school is in session. So I'll be awake early, and by 10 PM, I'm ready for bed. Despite it being summer, I have stuck to this schedule for myself. My husband will let her stay up too late. She is his little princess, and he almost never forces any issue with her (I have to be the strict one). I've told my husband to get her to bed before midnight; he did it maybe one night out of the last week.

School is going to be starting again for her on August 15. She really needs to get onto a more normal and healthier sleep schedule.

I don't know where to start.

Sticking to a regular sleep schedule is important, but it must be hard to do when your husband won't enforce it.

About melatonin, it's not really like a drug. It's a hormone that occurs naturally in the body, I take 3 mg at night sometimes and it helps.

Melatonin is naturally occurring. If your husband is afraid to do this then just add these things to your daughter's diet. Either he can work on resetting her sleep schedule or he can hear such advice mentioned. And deal with the fallouts when her moods are affected by her exhaustion.
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Has she gotten OT for her sensory issues? They can help with sleep management too. They can talk to your husband about the importance of sleep hygiene also. It will be really important for her to have a cool down routine before bedtime to help her relax and make it easier for her to get to sleep.

Aspergers often goes hand in hand with delayed sleep onset. It is not like classic insomnia, even if worry can happen because you are scared for the next day on that little sleep. My own issues started at puberty. I never got my hours in because I could never fall asleep on time. At the end I could fall asleep not way way too late but that was just because of chronic sleep deprivation.

If using melatonin, take breaks on weekends, that stuff might stop working otherwise. Also don't give too much to a kid.

Also know that Aspergers also goes hand in hand with autoimmunity and melatonin can trigger or worsen it. So it is not totally without risks. But IMHO sleeping on time is more important.

Routine actually does not fix delayed sleep onset, it just creates chronic insomnia and might superficially look like a fix.