Nothing is being omitted. As you said yourself, this is not the kind of writing where the author would omit particles. It is not even close to being that type of informal writing.
働きいい means 働きやすい.
This usage of いい is probably unique to Kanto dialect. It is not used in Standard Japanese, where やすい is used; therefore it may not be found in the dictionary. I hear this いい in Tokyo but not in Nagoya --- that is for sure. Around Tokyo, some people say things like 「このペン書きいいねぇ。= "This pen writes so well."」 while the rest of the country will opt for 「書きやすい」.
夫の働きいいように does NOT mean "to make the husband's work easy" as you said. You need to include とりしきる into your TL because that is what 夫の働きいいように modifies.
"(It was the wife) who managed things so that the husband could concentrate on his work."
The original does not say "concentrate" but that is what it means. What it is saying that the wife used to be the one that took care of the kids and the house so that it would be easy for the husband to work hard (without having to worry about the household chores).