As a random suggestion from someone who did manage to not get his children killed despite ADD... look into bullet journaling as an organizational system for parenting duties. Ignore the endless art-project nonsense on the internet, read the book, and focus on using it for task management and scheduling.

As an adult with ADD, it was a miraculous new perspective on tracking all the things I used to fail to do. I so, so wish I'd had it when I was dealing with small children.

I strongly second the use of a bullet journal.

I can't count the number of times while talking to my psychologist, in the middle of a breakdown thinking "If only there were a system that I could offload all of the dumb things I can't remember to do..."

...and then laughing my way out of the room because my wife told me weeks earlier that she wishes I were using my journal. She notices that I'm happier when I use it, she is much happier because she doesn't have to ask me to do something 4 times...

Thank you very much.

Using OrgMode for keeping my work-life in order has been a life-changer. But perhaps a bullet journal is more suited for keeping personal, and family life. I've never looked into them properly, but will definitely do so today.

I hear my partner is not the only one that worries? :)

I’m constantly playing the “no ones died yet on my watch” card.

It somehow doesn’t make her feel any better.

Amanda Palmer covered this well, in her song A Mother's Confession (which should make any parent cringe). It starts with her baby, whom she thought couldn't roll yet, rolling off a changing-table shelf and landing on the floor. "At least the baby didn't die" becomes her mantra, as the song details terrible parenting mistake after terrible parenting mistake.

As a ~15 days shy of being a father, I strongly second this request.