I’m so sorry you are going through this, truly heartbreaking my love. May be absolutely no use to you but this is what helped me in a similar situation.
Firstly, call your GP (or ask someone else to) if you think you will need help with sleeping/panic over the next couple of days.
If you can, look at the calendar for this week and delegate any organising, anything that needs to be cancelled/re-arranged to someone who has offered to help e.g can you phone and cancel or re-arrange this for me? You and DC will need space.
You might also want to ask someone to get food/meals or other shopping for you so there’s stuff in the house and you don’t have to deal with driving or supermarkets or transport. Ditto anything your DC might need this week and if you need to pay any bills/get money from the bank etc
There is no right or wrong way to react and the same applies to your children. The only thing you can really do is make some space yourselves away from work, school, activities etc this week. If you or the DC want to do anything you can of course but it really helps not having to explain what’s happened or to receive calls about missed classes, appts etc.
When you’re able - or again ask someone else to read it - there is information on the CAB website about what to do practically after someone has died, including when there is an investigation. This is different in England, Wales, Scotland etc so check the version for your country. CAB can also help with sorting out help for funeral costs, working out benefit entitlement, housing matters/council tax and anything else that might come up.
www.citizensadvice.org.uk/family/death-and-wills/what-to-do-after-a-death/