There's a lot of things going on here, but the ones that strike me are a) you are up early at 6, now some people's bodies are good in the morning , mine is not and even if I don't sleep, I'd still have problems with staying awake in the afternoon, this is not unusual, half my colleagues nap during afternoon talks b) what is unusual is that you then keep on sleeping. I'd still have a nap some days, but really limit it, you don't need hours and hours to become refreshed, just make it 45 min or 90 min (to have a whole sleep cycle or two) and then get up even if you feel terrible.
If you want to be a good mum, definitely look after yourself, self-care is hugely important (so exercise/gym good in my book), get a meds review, and more importantly keep interested in your children. I don't understand why you say you don't get much time with them/they are missing out- you are up at 6 with them, spend all weekend mornings til 1 with them at the very very least- for many working out of the home dads, that's more than they do.
So- I would try to limit your afternoon naps considerably using the behavioural techniques suggested here. You need to wake up and live the late-afternoon/evening too, by over-coming your habitual feeling of tiredness. It can be done- or at least, you don't have to give into it and nap for hours and hours, you could limit/cut out naps some days. The more you nap, the more you want to nap in the afternoon.
I don't think you are a bad mum, but talk of boarding is crazy at this stage, especially if your husband is fully involved. Better have parents around, I don't see what would be 'normal' about boarding, and plenty of families have one parent who isn't around as much for many reasons; disability, working away, they are lazy and disinterested, divorce.
I wouldn't change because you are a bad mum, I would change as it can't be that nice for you to live this life and I don't think change would be as hard as you think it would be.