There are a few things that have helped me sleep over the years, and I do have sleep issues. Light sleeper, had trouble falling asleep and trouble staying asleep.
I am now 43, and have to say it took until about 2 years ago to really get to a point where I sleep well.
1. I have a very strict bedtime routine, that I try not to waiver on, this starts an hour before I go to bed, includes getting my clothes together for the next day (so I am not thinking about what will I wear to work). Packing my lunch (again so I don't wonder what I will eat). washing my face/brushing my teeth, then getting into bed where I watch the news through the weather. Turn off the TV and read. I do not have a set time that I read, but try to be lights out no later than 10:30 because I get up before 6am.
2. White noise machine. I actually use an app on my phone now, but have used machines, and of course box fans. This keeps my tinnitus (ear ringing) under control, and allows me to sleep through the quieter noises. By the time my kids were your kids ages, they could cry loud enough to wake me with the white noise.
3. NO caffeine after 11am. Seriously. I used to drink soda and tea until the evening, and found that on the days I didn't have it after lunch time I slept better, and have found that if I am done consuming my caffeine for the day by 11am, it makes a difference.
4. NO NAPPING - This was a big change for me as well when the kids were small if I was home I would take one. It made me restless and sleep poorly at night. It makes me sad that I can't do this anymore, but is well worth having the good sleep at night.
5. Some sort of physical exercise daily or every other day. Even with your current level of exhaustion, the type of tired you get from using a treadmill, exercise bike, or elliptical is different, and eliminates all the nervous energy.
6. I do on occasion use meds to help me sleep. For years I took Benadryl due to allergies, it helped if I took it at bedtime, prevented sinus infections for me. It did not leave me hung over.
I was also on a low dose of Elavil/Amitriptyline for years for migraines, this helped with sleep too. After the A I found sleep was even more difficult because I would literally wake up and start evaluating my life, my decisions, his behavior all of it. The trick was to not wake up. Ativan is now my go to for this issue. I don't take it daily, but I do take it 1-2 times a week. It is the bomb. It allows me to fall asleep more easily, and sleep through without multiple wake ups, and even if I do wake up, I am able to fall asleep fairly easily. The other bonus is the dose is so small, that I don't get a hangover.
When talking with sleep specialists, the recommend good sleep hygiene, using your bed for sleep and sex only, I include reading before falling asleep, because if I read in the living room, I would find 6 things to do on my way to bed, and be fully awake again by the time I got there, cause that's how I roll.
Having a set bedtime, even on weekends until you build good routines and habits.
Having a set get up time, again even on weekends until you have a routine established.
No extra stuff in bed with you, so just the 1-2 pillows you sleep with and your covers.
NO co sleeping with kids or pets.
No stimulation 2-3 hours prior to bed
NO food 2-3 hours prior to bed.
If you lay in bed more than 15 minutes without falling asleep, get up and start your bedtime routine over. This resets your body and helps your mind to calm.
Some people swear by some herbal remedies, I never found them to be helful, but I am sure folks will be along with those soon.
One last thought if you try all this and it doesn't work you should see a sleep specialist. There are Many Many people out there that don't get good rest, and wake up frequently due to sleep apnea. There are significant health issues that come from having this untreated. So a sleep specialist is a smart choice to evaluate if you possibly have it, and how best to move forward if you do, or don't. Good Luck.