> two days in office to relax, three days at home to help wifie with kid.

This is not working from home, or working anywhere

If you think working from home means you have time to "help with the kid", you're wrong.

Have you tried actually doing that though. When you're at home you're always available to help out. If you're at the office its impossible. When your family is having a screaming argument next door how can you concentrate at home?

I don't know what you mean TBH.

If you are working from home, you are working. If you are helping out with the kid, you are not working.

I'm working when I'm working. Still don't get where you are going with this.

You implied you were maintaining a full time job (that's what I understand "hybrid" to mean), rather than having dropped to part time hours.