Still would have been caught. The SEC had already figured out he committed the crime because buying a stock before an acquisition drives up its price once is luck, twice is really amazing luck that borders on ridiculous, three or more times is obviously a crime. They already had enough on him to get a warrant to get info from his work, what they got just took away the "I'm a really really really really lucky day trader" defense.
If he wanted to avoid detection for every company he bought knowing it would shoot up in value he should have bought ten that didn't, sold one that was going to shoot up too early, etc. to induce some noise into the system. Though I'm not sure if that would have enough but at least it wouldn't have been so bleedin' obvious!
The other problem with his scheme was getting all his information from his wife. The SEC could probably easily determine that the same law firm was involved in all the purchases, and then zero in on his wife, then easily connect him and his mother. He'd need information coming from multiple sources - deals from multiple law firms, to make it harder to trace back. You know, like how the hedge fund guys do it (we all know some of them have to be doing this, but it is lost in the noise of their other trades so it pads their profits rather than being solely responsible for them)