If the context were just, basically, current job fine and new job is more money, I'd probably consider it a marginal offer: more money so can stop working earlier, but risk of more stress on wife and reduced family time in the short term.
However, in the context of unhappy at current job, likely to shortly have no job, and all candidate local jobs are 40+ minutes each way, new employer good and will cover expenses, I would consider this as a good offer. A couple of things I would do: be clear to myself and partner that it is undertaken on a trial basis, if it doesn't work out a job isn't worth excessive stress on the family, I would quite if that happened. I would definitely push for the 4 long days working option to provide long weekends at least every other weekend. With the extra money I would consider either partner having more paid home help e.g. with household chores, after school child care for child on some days etc., or, if applicable, allow partner to reduce working hours from full time to say 4 days a week, or finishing day earlier to match school hours. On the last point of paid help or partner working reduced hours, even a little bit might be a big benefit, and the cost only a fraction of your extra income.
I currently travel to client site 2 or 3 days every week for my job and it's 5 hours by train each way, with all expenses paid. I don't find it a problem, nor does my partner, though a key difference is we don't have a family. By comparison, a friend of mine who's a lawyer typically works 6 days a week, including 10 to 12 hour days Monday-Friday, which I thought sounded like hell on earth even though he's very well paid, but he remarked how bad my job sounds because I have to travel each week. So I suppose everybody has different opinions...