What is "correct" depends on the rules of analysis you're using. It would vary for different classes. For example, you write "Adj" but some classes would just use "A". In terms of content what you wrote looks OK overall.
Your "S1" actually should contain everything. Embedded within it, you can also separate out "S2" and "S3", but if you're trying to understand how everything fits together you should start by distinguishing whole constituents (including everything inside them). So personally I'd probably start by separating out the subject (your "NP"), then working on what you're calling the "VP" above, including also "S2" and "S3" within that.
(But again, maybe there's a reason based on how you've been taught or expectations for you class about how you should approach this. For this kind of detail-oriented analysis with "correct" answers, asking online is generally NOT very helpful. We can discuss big ideas, but it won't necessarily get you to the "correct" answer for your class.)