P.M.
Oh dear, my, my stomach clenches at your husband's suggestion to lock your toddler in her room and leave her to cry. If it's not her fault that her schedule is messed up, should she be punished for it? And the simple truth is that some children just sleep more poorly than others. She may have inherited that from you (and you wouldn't lock yourself in your room when you can't sleep). But a few things may help shift her days and nights:
Shorten any daytime naps she may still be taking. Give her at least 20 minutes of sleep to recharge, but don't let her sleep for more than 1.5 hours (a time period that will give her one full sleep cycle).
Getting her up a bit earlier each week might help, too. Open windows to daylight and turn on lights in her room to help her wake.
Get her out in plenty of daylight during the day; the light she'll get in the blue range helps reset the brain's sleep/wake cycle. Keep evenings in low light, with NO TV or computer time within 2 hours of bed. Those screens give off light in the blue wavelengths, and will keep her brain from producing natural sleep and relaxation-inducing hormones.
Give her as much physical play during the day as possible. Her body will want rest by nighttime. Before bed, keep activities calm and relaxing. Extra snuggles or soft music might help. I know a mom who uses yoga sessions with her very active son about an hour before sleep, and it seems to help him settle (immediately before bed, any kind of exercise might be too stimulating.)
Your daughter probably won't learn to sleep if left to cry. She might learn to give up, though. I strongly advise you against it.
ADDED ––––– I intended to write this first, but spaced it out:
Keep your daughter's bedroom as free of chemicals as possible. Ubiquitous scents and ingredients in common household cleaners can seriously disturb the ability to sleep in sensitive individuals. Google "green living" or "healthy home" for lots of suggestions. (You might want to follow these principles in your own bedroom to see if it helps your sleep, too.) I'm extremely sensitive, and have eliminated ALL synthetic chemicals from my house. If I get exposures out in public, it can wreck my sleep for two or more nights.