I'm sorry about your dad passing away. I've had people close to me have long illnesses or go quickly. It hurts just as much either way. I'm afraid there is no easy answer or quick way thought the grief. It tales a long time, hurts, is frightening and makes the whole world seem almost remote and even hopeless.
I guess there are some things that make life a bit more tolerable. The first might be to understand what is happening to you, the common stages of grief. Someone experienced in that area, a counselor, might be useful.
You talked of thinking of death and losing the kids and ones you love. That is exactly to be expected. I became very concerned a family member be distracted driving and have a fatal accident. Nothing happened, my thinking was distorted reacting to the situation.
Another thing I found particularly good was burying myself in my work to keep my mind occupied. I don't know your circumstances but there is probably something that fits the bill.
You talked of being strong for everyone, try to shed some of the load and not demand 100% of yourself at the moment. An example might be that rather than being the comforter to somebody else just cry with them, don't consciously try to help. Your presence will help anyway.
You have a large family, your mum plus 5 siblings, also a husband and 4 kids. True they might need support, but they might need to support you and each other too.
My preoccupation at the time they passed away with the death of someone I cared about was just concentrating on one thing - unavoidable at the time. It masked all the rest of the memories, good ones and all. I can look back now, sometimes sad, sometimes happy and see their life as a whole and my part in it.
In time (yes that horrible phrase) you will get there too.
Forgot to say - I repeated myself endlessly to anyone who would listen, grief does that.