I'm so sorry to hear this OP.
As pp's have said you have nothing to feel guilty about.
My GF was determined to die at home and also refused carers.
My GM was adamant his wishes be respected despite my DM's and my views otherwise.
My GM, DM and I worked "shifts" for just over 5 weeks (I took unpaid leave from work as did DM) and my DF pitched in around work as much as he possibly could.
I've never been so physically/mentally/emotionally broken as I was at the end to the point I couldn't really grieve because I was just relived it was over (and I was in my mid twenties no children). It took me another 6 months I'd say to actually start to mourn properly having finally shed the trauma of that time.
The idea of shifts make it sound feasible but it just wasn't. At every crisis (usually pain management related) we'd all pitch in and there were periods we were had no real respite for days at a time and they grew more frequent towards the end - by which time all our reserves where utterly depleted.
It was so very hard and my DM and I had the added burden of a huge worry that we'd lose my GM as well through the stress of care in her 70's.
In truth I didn't want my last memories of my much loved GF as being responsible for intimate care or being in pain as we waited for HCP's to get the house to help him.
I honestly feel it would have been best for DM, myself and GF if he'd gone to a hospice.
However that said, it wouldn't have been best for GM.
Despite the toll it took on her she derived a great deal of comfort from knowing she'd looked after him until the end.
Also witnessing his decline so closely (she said) made his passing easier because she knew "it was time" and she really understood that his body couldn't fight any more and we'd reached a point where to keep him pain free was getting into the territory of being lethal in itself.
Would I do it again? No. But I don't think I'd ever have to.
The experience made me DM/DF very sure that if we were in this situation we'd want hospice care, not only for ourselves but for our loved ones.
So again I'm sorry
.
It's really tough and you've no reason to feel guilt at acknowledging that. It's also ok to feel angry (as I and DM did) that the patient is making choices that had an impact they didn't fully appreciate (and in latter stages probably wasn't aware of) on those they love (especially adding to be burden by refusing carers).
Try and look after yourself as best you can. I remember making big pots of soup that we'd all just help ourselves to at various points in the day/night without "cooking" (something about eating soup at 4am felt better than a sandwich and warming in the winter).
Most of all be kind to yourself mentally. You feel how you feel and it's not right/wrong - it just is. 