Itsboiledeggsagain - why do you think it unreasonable that a FATHER ask their employer for adjustments to accommodate childcare? Millions of women do so and as long as he's putting in the same total hours and it's not affecting his work - which in most workplaces it wouldn't - then I genuinely don't see the problem.
We HAVE to stop acting as if fathers aren't parents too. We have a shamefully poor set up compared to many other countries regarding fathers employment rights and expectation to provide childcare.
3 months is NOT long at all when you consider in other countries fathers can get up to 3 months paid paternity leave!
Op you REALLY need to stop saying and viewing it as "help" - and telling dh same. Words have meaning. He's not "helping" you're not asking him to "help" you are reasonably expecting him to PARENT because he IS a parent - to TWO children now.
He seriously needs to get on board with that FACT!
A good father takes an interest in their child's education, development and meeting their needs - he's doing none of that.
"Breakfast club could be useful if the school has one. Sharing the school run with other families (you would be helping them as well) and the idea that DH drops you all at, or near, school might work?" I agree these ideas are easier and cheaper to put in place short term.
Medium to long term however, I agree driving more important than moving. Not only for school but as you'll soon realise children your eldest's age tend to start wanting to do loads of extra curricular activities plus things like parties etc ramp up and with 2 children and such a big age gap you will find life SO much easier being able to drive. It may even mean you don't need to move.
But even so 1 mile I'm afraid I also think isn't that far and I'm shocked if it takes an hour! I have a driving licence but at times have been on meds that meant I couldn't drive, dd has mainly walked to school even when I was driving as she preferred to go in with a gaggle of friends. I've just checked and the distance was 3/4 of a mile and took her - even with their slow pace and mucking about - a max of 10 mins. Uphill all the way home too.