Commuting to Hatfield from further north (Stevenage, Hitchin, Biggleswade) requires travelling on the a1 which is an absolute nightmare if you need to commute at peak times. You would generally need to add an hour on to your journey time.
However, Hitchin has some really lovely areas if you are prepared to withstand the commute.
Welwyn Garden City is very mixed - it has some lovely areas and some very dodgy ones too. If you manage to stay the right side of the town it is nice and has quite a village-y feel to it.
Hatfield - as I'm sure you have worked out - is pretty much a no-go apart from the Hatfield Garden Village area which is very nice but I believe leads to a problem with good schools.
St Albans (a 10 minute drive) would be your best option for schools and is a wonderful place to live. It is pricey though and still has some avoidable areas ('Cottonmill' and 'Newgreens').
Some other places with a short commute worth considering would be Hertford, Park Street, Knebworth, Wheathamstead.
Am not that knowledgable about schools, hopefully someone else will be along to advise on that. Anything else you'd like to know I'd be delighted to try and help.
Good luck with the move!