Your family needs to go into grief counseling. I don't think you have a clue about what is still yet to come. Things may seem fine right now with the others, but the grieving process is long and arduous.
You better prepare yourself for when things finally sink in and crash for your daughter and the other children. They are are all going to express their grief, anger, and other emotions in different ways, but they're all going to go there. Some if not all may take years to get over it.
Your thinking the child is purposely misbehaving or is in some way a spoiled brat is unfair, and will cause unnecessary turmoil for your daughter and her children.
The best advice is to encourage ALL of them to go into grief counseling. If necessary, you should join them or at the very least read about the stages of grief. It is especially hard on young families and couples because psychologically people are not prepared for the loss of loved ones when they are young. Your daughter lost her lover and spouse. She may be smiling and seem normal, but I guarantee you, she's pining for him when she is in bed alone at night. She is probably in no condition to help comfort her children well either. And for children, they have no life experience as of yet to draw upon to help them reason with the fact their father will not ever be coming home again.
They need a neutural party who understands grief and it's many twists and turns. Not only are they dealing with death..but also the tragedy and turmoil...maybe even guilt that comes when someone commits suicide. If they don't learn to face it in a healthy way, it could turn into something serious. It isn't unheard of for widows to develop spending addictions, chemical addictions, or for children to become violent or angry during grief. Those emotions that aren't dealt with in a healthyway will and do come out sideways.
Be the strong one for them right now, and find them the proper help they need to get through this tough time. Avoid taking any of their behaviors personally, or as fits of selfishness or being spoiled. It's not about you. It's about the fact their father is gone and now they have to deal with what that change means for them and the rest of their lives. That is a lot of a kid to deal with.