OP, I presume if you change your teaching job to a closer school you will have to pay back any extra maternity benefits? Or maybe you don’t get anything extra anyway.
I would definitely consider having one person closer to home if possible, and prioritise the Farringdon commute.
I would say things that make a commute easier are only getting one form of transport. So being able to walk to the station each end is just so much easier - I would look at somewhere on a direct line to Farringdon.
The other thing is that if the trains to where you live aren’t very frequent, it is completely soul destroying waiting on the platform for 58 minutes for the next one because you were delayed by 5 minutes at work. I personally would choose somewhere with at least 4 peak time trains an hour.
Royston, Herts might work. Market town. Nice countryside around, should be within budget for a house within walking distance to the station. Direct train to Farringdon. Fast, frequent trains to Kings X, so if you end up having to commute to Vauxhall, you can get the Victoria line.
Other train lines nearby, so if there’s a problem on the line from Kings X, you can still make your way close to home from Liverpool St.