[rewboss]

In the second sentence, I would add a comma after "writing", but that's probably optional.

Without seeing the rest of the text -- or at least a paragraph or two -- I can't say which is an improvement. But they actually mean slightly different things.

The first sentence is a simple statement of fact. There are two things you need to do: look at some sentences; and break the sentences down.

The second sentence states one thing you need to do -- look at some sentences -- and the reason you need to do that -- grammar is important.

Those are two completely different sentences. Your wife has probably edited the whole passage, moving information from one sentence to another, combining some sentences, separating others. It's impossible to say.