I'm so sorry for the pain you're going through. I lost my mom in a car accident. It was unexpected and still hurts deeply.
Take the time you need. I personally would use the family/sick days (five in my contract with pay; which in my years of doing daycare have never claimed, keeping them just in case of an emergency).
And if you need.more time take it (obviously parents aren't expected to pay for those).
Just for guidance; agencies policies are, parents pay when the caregiver is available. In my husband's work they give just one day and three max. If it is a very close relative.
Also being sensitive to others, maybe your clients do not have jobs that allow them to have extra sick days. Not all work for the government with greater benefits. Some are like us self employed and need to make their ends meet. They might need to pay someone else to care for their child so they do not loose on working days. I would just probably let them be at least they will be there when you come back.