Will doesn't 'provide' for his family because he wants to make them happy, he does it because he wants to feel superior to Joe/Eddie/Ed
I think its more nuanced than that. Its not so much about "superior" as "doing better". He is proud of providing for a family with an honest trade rather than being dodgy and feckless like the other three. I see no difference there, in Susan being proud of "dragging herself up in the world" from being a Horrobin to being a home owner and honest worker with two hard working, honest children.
However he has always been insecure, lacking in emotional literacy and has been raised by the Grundys (including Clarrie) to have a very mysoginist view of women's roles. Its not surprising he reacts in the way he does.
Yes Will sacking Pete was a clear signal that Will chooses to be ‘too busy at work’
I'd say that is a good example of the insecurity. Martin has no compassion, would cheerfully chuck Will out if profits go down. Martin has told Will to cut costs. He interprets Pete's helpfulness as an attempt to take his job.