Op, you sound like a normal parent to me! I had a 2 year old and a new baby and and I look back now and wonder how I managed with no tablet:)
Forced to watch Pingu whilst bf ( or reading stories when exhausted with being up all night with one or the other or both) instead of morse with pfb, for a start:) or my interest in late night snowboarding competitions whilst bf pfb, curtailed by yelling toddler, baby yelling too:)
I found it useful ( still do) to have a flexible plan for days, up and out, lots of snacks and drinks, very flexible, no panic to meet anyone and timing- feeding ducks, park, all low level stuff - and tea and cake at friendly garden centres which have a play area. Pick your activities, dc that age get excited about a puddle walk:) and I introduced " mummy time" where they watch TV or whatever and I have a coffee and NO TALKING. It's only ten minutes but it's a good thing.
Saying "gosh, you're really upset and angry, would you like a hug and we talk later?" helps. Plus showing them how to play together. And watching Charlie and Lola really helped my ds with How to be a great brother. As dd says ( at 5) " tv, mummy, is very educational" and it is. In small doses.
Relax a bit, op, you're clearly self aware- and 123 magic is a great book, as is toddler taming, ( bad title I know) and how to talk so kids will listen, and kids will talk, raising girls, raising boys- you don't have to wait til they are a nightmare to read them, btw. Just having the knowledge of their development ( and hormone burst, they can't help it, nor the reaching for independence - supported by you and your dh/DP)
amd totally- I was an amazing parent before I had dc:) mary Poppins would have been green with envy:)