Real true sleep deprivation has less to do with # of hours but more the quality of sleep you are getting. With children waking up the chances for quality restoritive sleep go way way down!
Get a book on good sleep hygiene - naps, sleeping in don't bank sleep in the sleep bank. its getting the best night time sleep possible. Look at your sleep environment and how to make it better for you (temp, light, matresses snoring partners
Ask for a sleep assessment referral as well as a blood workup (something like anemia could really mess with energy levels), they can be done at home you just wear the machines home very sexy! It might not be your lifestyle but your sleep itself that is compounding your issues - I have narcolepsy myself I wasn't dx until after dd was born as I found a way to manage before children but with children messing with my sleep I could not I have met many people with apnea, insomnia who didn't realise it until they had kids how much bad sleep was giving them what they call EDS excessive daytime sleepiness.
most people allow their sleep to suffer and try to plug through the day sleep is very important to health. There are many natural ways to manipulate the quality of sleep as a narc I have to go the opposite I have to keep my sleep light as I dream more than I should and am in deep sleep far too long so stimulating things help me (radio on, lights on, cold rooms, full bladders etc). Most peole need the opposite dark, quiet as they are trying to promote more deep sleep not less.
Also remember its not the hours of sleep but quality to say I only got 4 hours of sleep doesn't mean much you can sleep for 9 hours but if the four hours was better quality not interuppted.....I digress
I ban clocks from my bedroom as well as I find if I have to get up at 2am I feel more tired if I know the time