If you need to be in MK for work, really, I wouldn't go too far from MK. I'm with you on MK itself, I wouldn't want to live there but it is useful for John Lewis and other facilities. And it's not far to London driving or by train.
Things to think about:
Parking in MK is terrible, is there parking with the job? If not, work out where he's going to park and how much it will cost (I know you're used to London though)
MK station and commuting to London is fine in theory but in practice the service is terrible, the trains are often delayed or full or not working and it can easily take 2 hours from Euston to MK. The parking at MK station is expensive and gets full by 8am some days
There are some really nice villages & towns around MK: Stony Stratford, Buckingham, Olney, Winslow. There's supposed to be a new train from Winslow which will go to MK / Oxford so bear that in mind although it's currently delayed by the unions arguing with Network Rail (there aren't enough eye rolls in the world). Winslow is a nice town.
I'd say the commute from St Albans is do-able but not great and if the M1 is fucked everyone goes on the A5 so that gets snarled up too. St Albans is lovely but expensive.
From MK Birmingham isn't too much of a drive but you really wouldn't want to commute it. But fine for visiting family. I wouldn't base where you live on family help with childcare unless your family have 100% agreed to do this, but maybe they have.
Here's a nice house in Stony (but no parking and only 1 bathroom)
https://www.rightmove.co.uk/properties/168309956#/?channel=RES_BUY
Here's another, near Olney
https://www.rightmove.co.uk/properties/163119284#/?channel=RES_BUY
Stewkley
https://www.rightmove.co.uk/properties/170747519#/?channel=RES_BUY
Buckingham
https://www.rightmove.co.uk/properties/170573978#/?channel=RES_BUY
https://www.rightmove.co.uk/properties/167320184#/media?activePlan=1&id=media19&ref=photoCollage&channel=RES_BUY