They're kids for what seems like minutes pal, mine are 9 month sold now (twins) and I'm lucky in that I have a great deal of flexibility regarding hours. Having said that when I'm away I do miss them terribly..
Just an alternative point of view, If I have a busy day then invariably I'm away prior to the kids getting up and find myself driving like a dick in the rush hour to get home prior to bath/bed time to see them not always successfully.
So consider..... some commuting, a cheap guest house, a travel card...... your principal job is to provide for your family, if the London job is more secure with potentially more prospects that may pay dividends later...you may be able to have more flexibility over hours or even working from home.
My dad was in the merchant navy and spent weeks away from home at a time, he always made a 300% effort during his time at home and there was four of us!, there is the quality not quantity argument as well.
Sounds like you've made your mind up follow your heart and good luck with it