I think it's totally possible to do all on your list if you work a 35 hour week. At this point I have to say I have an easy 20 minute walk to and from work, so no commute to tire me out.
1.give your child/ren your undivided attention
For me the answer is to get sons into a late-ish to bed, late-ish to rise routine - bed around 8.30 - 9 for nearly 6 year old. Later for 112 year old. They wake up around 8.00 am.
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exercise
I used to run to work, will do again once heel injury has cleared up.
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rest
get around 7 hours sleep a night, no problem
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have "you" time
Lunch hours, time when work is slack and I can catch up on other stuff, but my main 'me time is the early mornings, when the house is quiet. I get up around 6.00 am so have untill 8.00 am to do what I want. Mumsnet usually wins over housework.
5 do the housework
See above, but I have the odd blitz at weekends, and tidy up with dh during the week.
Yes, at times I do feel frazzled. But it is manageable, especailly as the boys are getting older and more independent. I am sure I would still find other things to frazzle me if I worked less hours.
I have a friend with two older children - age 8 and 12. She has only ever worked a short hours 3 day week, citing the the reasons you list. It is her life, but I don't go along with her logic, tbh.
Recently I had to button my lips when I heard her half jokingly nagging her husband (who works a long 5 day week) about why he gats so little freelance work on top. Talking to her, she was unhappy they did not have more money as a family. The answer seemed obvious to me