The relationship is good otherwise, am I overreacting or is this a valid reason to end a long term relationship with kids involved?
The answer is all in the nuance of the situation. If you are both contributing fairly equally to the household but his contributions are done in a half-arsed way that regularly cause unnecessary stress or result in you having to do extra running around, then no, you're not unreasonable to think he needs to improve.
The big question though is whether separating genuinely would result in an overall easier life for you. Maybe there would be less stress in terms of having to clean up after him, but if separation also would mean you have to work a lot more to cover the bills, then it's not a simple equation. Maybe the answer is that it's easier for you to do the school runs if this is a particular sore point, and he can take over more of a job that he is competent at doing. If he's genuinely incompetent at most things then yes, maybe it's easier for you to separate, work more and have a couple of days completely free for yourself when he has the kids.
You just have to be really honest with yourself about whether you're exaggerating his overall failures and your overall contributions or not.
I think you're over reacting from what I've read if your relationship is good otherwise, no ones perfectly organised all the time, losing shoes in the morning happens, I can't remember how many times this has happened to me.
But this is also a matter of nuance. There's a big difference between 'not being perfectly organised all the time' and having to hunt for shoes once a month or so, and being so disorganised that getting through everyday tasks/routines are more often interrupted and chaotic than not.