First I want to say how glad I am that your niece, nephew and sister have you in their lives. Your love, concern and compassion will be the thing that helps them now, and in the years to come.
I don’t think there is a particular formula for this, but being there with them and sharing their pain is ultimately what they need the most for getting through this.
Your niece is at a different developmental level than your nephew and they may need a different approach to being told and being comforted afterward. In general a young child’s emotional reaction and needs in the situation is more functional than the emotion of the adult reactions and feelings. By functional, I mean children often want to know when they lose an important adult in their lives what changes will happen for them. Letting them know that their needs are still going to be attended to by those caring for them is often a great comfort. Children grieve differently than adults when it comes to loss, and I would strongly recommend you find a therapist who has had direct, specific experience with children dealing with loss and grieving. Children have different verbal skills and often need alternate means of expression. One of the most gifted therapists in our area is a creative arts therapist who uses the child’s artwork as the vehicle for expression and communication.
In the meantime there are several good books for children, including Tear Soup. I have linked a list here for you of the others. Stories are one of the best ways children can relate to the loss, and may be helpful in breaking the news to them about their father’s death.
My heart goes out to you and your family at this time of grief and transition.
Wishing you patience and peace,