Hi dear I am sorry for the great loss, may your father soul rest in peace and let the God give strength to your family to accept the loss.
I understand at this crisis it isn't easy for your mother to forgive and move on with the situation, she is going through distress with the loss and along with, environment situation might add fear of her own health, which could be that she doesn't want to leave her children alone.
It is something she is anxious, sharing her feelings could make her calm.
Also she needs to try coping with the situation, engage in her household work or the activity she loves to do. Involve with other family members, avoid discussing the loss or reason for your father's death.
Take care.
Next Steps
In the meantime take the help of an experts to guide you through the process of healing.
Health Tips
Yes it could be the common and difficult situation, but we have to lead the life in positive manner, she can do rangoli before her sleep, might make her sleepy, avoid having coffee or tea at least 5 prior to sleep, chant omkara mantras or breathing exercises, pour out emotions through writing or sharing with comfortable person, build the confidence of her own health. Gardening or cooking or any hobbies will help.