Hi Raye,
So sorry to hear about your dad. You are right, losing a parent is one of the hardest things you can experience. All the thoughts and feelings you describe are ones we all go through, I think. I know I recognise all of them. I think this is probably a very normal response to loss. Karena is right, it is still very early days for you at the moment, so I am not surprised by the degree of pain you express. It may sound like a cliche, but all you can do at this time is try to be kind to yourself and patient too. You did your best, clearly and blaming yourself in some way is a normal reaction. The truth is though that you did all you could believing it to be the best and it was. You couldn't have changed the outcome and we all lose our parents in one way or another at some time. Much as we would like them to always be there, that just isn't possible.
I know you say it is hard to go back to the family home, but please try not to leave your poor mum alone too much either. She will be experiencing as much shock and pain as you are and possibly more, as he was her husband. You need one another and can help one another. You will be able to help support eachother through this, so use that. It will help.
I found after I lost my mum in 2017 that it helped to make an album of favourite photos of her and some people start a memory book, writing down accounts of times they spent with the person they have lost. I didn't do that, but I did keep a journal of how I was feeling and what I was thinking every day and found that just writing it down helped get it out of my system and helped me feel better, so you might try that.
Time does gradually bring acceptance and the memory of those final days do recede gradually as you recall the good times more clearly as time passes.
You are not alone, Raye. Sending you a hug..xx