There is no magic bullet here OP. I’m afraid you need to make some tough choices. No one has it all.
In reality if you want to be there for school drop offs/ collections - you are looking for a career that gives you that flexibility. Which More companies are offering as a result of the pandemic. I see some companies offering permanent wfh contracts, or experimenting with core hours of 10-4 (with flexibility outside of that). Even those however won’t help you with school holidays/ inset days/ child being unwell etc. This is also largely dependent on the sector you work in - tech/ software related roles are desperate to retain/ promote female staff so if you looo at different sectors, you may find it easier.
In terms of career progression, I’m afraid to say that I know no people who have managed to work flexibly/ part time and simultaneously climb the career ladder. That may change culturally nowadays but to date has not happened in my experience.
I personally worked PT when my children were pre school (and I subsequently saw my career stall during those years). Once they were in school I went back full time and my career has progressed brilliantly. It has however come at a price: I didn’t do school runs, I have missed sports days/ assemblies/ prize giving and even a birthday.
I don’t have any regrets as it has afforded my children and I financial security. And now as my children are increasingly independent, I have something outside of them.
How Did I manage? With a team of help and with military precision organisation. My career and my kids come first and second. Hobbies and a social life have also taken a hit as a result of my choices.
My only strong piece of advice? Please, whatever you do, don’t give up work. It may be hard but try and make this work. Even if you just stay in part time work and did as I did (which was just stay at the level I was), it’s better than stepping out completely.
Your husband also needs to step up and divide and conquer the school runs etc.