1. You and my daughter want to marry, I know.

2. I know you and my daughter want to marry.
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Does #1 mean #2? When do you use the #1 expression.

They mean approximately the same thing, but #1 is phrased a bit awkwardly. Out of context, it's not always clear. #2 is by far the clearer sentence.

Context would be needed for understanding #1. A possibility might be if a young man were talking to his girlfriend's father and seems to be taking too long to get to the point! So the father might say, "You and my daughter want to marry, I know. But where do you intend to work and live?"