Sorry to hear of you loss of your father. It is never easy, but time helps. Concentrate on the funeral and being there for your mother. It is always whirlwind of activity for that first week after a death. I know, been through it with both of mine. Especially with my mother who died very unexpectedly, my sister put it best: it was like planning a wedding for 300 plus people in less than a week, but you don't have any idea how many folks are actually going to show up. In our case it was near 500 for the memorial service. We did not have time to really grieve and realize the while situation until the following week or two. I imagine for you it will be similar since like myself, you are out of state to deal with everything. That makes it more difficult right away.
I know you actually volunteered for the layoff, and even though you know it was coming, it is still stressful in itself. Keep the health ins with the COBRA for now, and you can deal with other options once you get back to home and have had time to settle back to a bit more normal. Your boss knows you are not available right now, and those employer paperwork and leaving employment paperwork can wait.