I am near a landline 90% of the time, am reachable by internet during working hours on weekdays, and go to my desk to check emails and chats multiple times a day on weekends. It turns out you do not need to be reachable or online every second of every day to do virtually anything in the modern world including raising kids.
Oh, this sounds like you work from home and can just substitute your landline and PC for 90% of contact, this wouldn't nearly work like this for most people.
I had this lifestyle when I worked from an office, and at home, in both individual contributor and leadership engineering roles. I also travel quite a bit.
Just set expectations with others and it works just fine either way. Only thing in the way is cognitive dissonance for most people.
In my case people absolutely forgive not being able to reach me every second of every day because I am a productivity machine due to being able to actually focus.
Back them, they did called you to work and it was customary to rely message by two other people. There is no such desk anymore and they dont want to be handling your life.
And if your kid needed to go home and sleep in bed, you had to take the day off instead of home office. There was price to that.
Oh, and back then school did not expected parents and kids to have phones, now it does. Information about schedule changes, homework, what needs to be paid and such is broadcasted with the assumption that everyone has a phone.
If you have an unusual lifestyle choice, you simply need to communicate that to all involved. Any that do not respect it, you can seek out alternatives for.
One clinic denied me for not having a Google or Apple account, so I took my business to one that would accommodate me.
Rolling over and doing what the majority of people want you do to is not how change happens.