Well if it is the better paid job, it is important.
Absolutely, so she needs to clarify that.
He IS being selfish if he remains in a low paying job which doesn't allow him to share the parenting load.
From what I've read, the only thing he doesn't/can't do is help in the mornings. OP has said he does his fair share of housework, after school jobs, bedtimes and weekends.
Not everyone has the means to get a job that's well-paid with lots of flexibility. It doesn't make them selfish.
His wife is struggling and the thought of returning to work and carrying the stress of every bit of childcare when there could be an easier way is stressing her further.
But we don't know if there's an easier way - theoretically, there may be, but you have to be realistic. Very few people can just walk into a new job that's well-paid and flexible.
Childcare may be stressful but so is working full-time and supporting your family. I don't think playing stress top-trumps is helpful, really, especially as OP does say he does his fair share outside of work.
He is selfish if he refuses to explore options.
Is he? Should he do a job that makes him miserable so that OP has help for five hours a week?
Or is being flexible only the job of the woman.
I don't think anyone has said that, have they?