I'll be honest with you
I assume you are a bit younger than me - and I think working 3*12 hour days, plus a few extra hours on your days off, should be more than do-able without getting as exhausted as you are.
I suppose a lot depends on what time you go to bed - but I assume that as you say you are flopping in the evening and not doing much then you are getting a fair bit of rest in teh evenings anyway.
Are you sure that there are no general health issues at play?
I suspect that what you really need to do is get organised and have a proper routine going, so that everything stays manageable.
So as soon as DD is in bed each evening, you do one thing properly each evening!
Day 1 - 1 hour doing on-line shopping
Day 2 - 1 hour doing general clear up
Day 3 - 1 hour putting away on-line shopping - clearing fridges etc
Day 4 - 2 hours ironing, 1 hour general cleaning
Day 5 - 2 hours bulk cooking, 1 hour laundry
Day 6 - 1 hour paperwork
Day 7 - 1 hour tidy up ready for week ahead.
That leaves you 3 hours on each non-working non weekend day for marking/me time which is loads of time, and it leaves the weekend almost completely free.
If you are doing 3 hours a day extra work on teaching days which it sounds like you are if you don't pick DD up until 5.30 and you are doing 2 hours extra on non-working days that adds up to 10 hours additional hours a week - which on a 3 day week is surely plenty!
If you continue to feel so tired though, then I think you need to look at getting some medical help - it sounds rather unusual to me to be so tired on the kind of hours you have described here.