Echoing others, I'm so sorry for your loss, there aren't really words that comfort fully I know, but I found some solace in that you are not alone and posting your thoughts and hearing others experiences can be of help.
I can only go on my experience of losing my DW to cancer earlier this year and we have 2 DC - and reading your post, sounds very similar.
I found tackling the formalities in sections, concentrate on doing and closing out a couple at a time, def use the tell us once service, that helps.
It can take some time to work through, but in a way, I found it a bit of practical distraction and helped me, but everyone is different. Also, try not to do too much, I think I did, which was okay in a way but also I look back now and think, it added some stress.
One thing I think looking back is; don't second guess your emotions, it's ok whatever you feel, especially with having DC. It's ok to feel 'ok', it's ok to be upset, cry, frustration, but ultimately, this sounds contrite I know; look after your DC and yourself, that's really what matters, it'll be ok, it will.