Grief is not a private family matter. That belief is an outcropping of cultural denial of death. Most folks do not need time alone to work things out Solitude prolongs the grief process. Being alone is generally the last thing needed. Make yourself available.
Survivors lack self-extrication skills.
If a gesture is declined, receive it as a temporary decline. It is not a final response. You are dealing with a process. Show up again. Remember to talk about the deceased.