In The Godfather, did Michael Corleone's mother know what was going on in the family?

Yes, absolutely. Vito Corleone's career may have started with his entanglement with - and murder of - Fanucci, but his status as a "Man of respect" was kick-started by his wife. There's a key incident in which he browbeats a landlord who was about to evict an Italian woman because she had a pet dog. In the book (I think the film glosses over this bit), Vito comes home one day to find this woman with his wife. She (Mama Corleone) asks Vito to help the woman - presumably in the full knowledge of what form this help will take.

She would certainly have had a pretty good idea of his line of business, but in that time and place it wasn't a woman's place to question her husband, so she would not have known every last detail.

You have to watch Godfather II. There you see how the young Vito Corleone becomes the Don. But more subtly you see how his young wife becomes the woman in Godfather I. Women had it very hard in the late 1800's and early 1900's. Early in life they had to work, then when they got married, they had to raise the family. Family was number 1. If the husband provided, no matter what he did to do it, the wife did not ask questions. Very complex.

Young Vito is very dedicated to his family and obviously loves his wife. That was critical to her, not how he made his money.

I wouldn't say she knew he was in Costra Nostra......but she knew he was connected.........

Women know who they marry.......in the early days she had to know Vito was a crook.....to what length is another story.

After the kids and lavish lifestyle you start to question less.

No, she thought the family were pork butchers.

Italian women knew what was going on. Not every detail, obviously. They were smart enough to keep their mouths closed and their opinions to themselves.

I think she might have been suspicious (and probably knew full well) but she would never have questioned it - it would not have been her place. She spends enough time praying for Vito, so I expect she felt she needed to.

Who'd have though olive oil importation would be such a high risk occupation?