I have been there in some ways..... my dad died about 2 years ago from a stroke.... and he had been suffering for years from one ailment....
What matters most, is what you are doing now.... it is hurting so bad, yes, and it will not get easier..... There will be lots of regrets.
I regretted not calling my dad in those early years more often... we lived in different countries but I avoided calling him because I didn't and couldn't bare to hear his pain or ailments and wanted to avoid speaking to his de facto.
When my dad had a stroke it was just after I called him and shared with him of my marriage break-up . His defacto later insisted and blamed me that my dad was so worried for me that night that it caused him a stroke.
Deep down I cannot help but also blame myself.... for everything, just like you, but there comes a point in your life.... that your thoughts kick in.... do you carry that baggage and destroy yourself or try to be a better person to the other loved ones who depend on you? You have your fiancé...... you need to not blame yourself.
I have my child who depends on me.... do I let those thoughts get me down.... I cannot.
The best thing right now is to be there for your dad, and even your mum. When they say those hurtful things.... it may or may not be true... but know that they too are hurting... It is often easier to 'blame' someone or something.
But the reality is we are humans, we get sick..... you cannot turn back the clock, you have this last few weeks or days with dad..... be with him. Pray with him. Hold his hand, if you want to, seek his forgiveness.
My dad died from a stroke without opening his eyes to acknowledge my presence. My heart broke and is still broken when I think about it.
The only thing is God who is there for me, who in the back of my mind, forgives me, and I know have been forgiven.
You have the time with your dad now, even how short... tell him you love him.
God bless, and I will keep you in my prayers and thoughts.