Dear @maxabit, I am so very sorry to hear about the situation your family is going through at the moment.
The loss of a loved one is indeed a tough reality to face (particularly when unexpected). I really appreciate a point you highlighted here, which I think it is very important for all of us to be aware of :
I guess is a sort of mild depression since it takes a few days to come out of.
I feel that nowadays, the line between sadness and mild depression is rather blurred, and one can easily morph into the other. This is precisely why bodies like NICE recommend caution when prescribing medication in cases deemed as mild-depression. In your situation, it is a most natural response! You are grieving, and you will go through different phases and overcome it at your own pace.
I am also glad that I have always taken steps to move out of mild depression phases so that I don't progress to a form of severe depression.
I am so pleased to hear this. Remember then brain-mind assumption! Brain-activity-patterns respond and change to mental events. So, there is a time (for some sooner and for some later) when we do need to move on. When we dwell for too long in that painful feeling our brain-activity patterns change in a way that leave us stuck there. So much so that we tend to forget the good things in life. This is a well-established notion in psychology, which has also to do with the hippocampus - an area of the brain that plays an important part on the functions of short-term and long term memory!
Exercise is indeed a great way to help you through this, among psychologists it is sometimes termed 'a natural anti-depressant'. Also, not long ago you posted a great, practical article about meditation. The hippocampus (and many other brain regions) also 'love' meditation :D
All the best to you my dear. I send my thoughts and love to your family.