All very good, constructive responses above. And I'll agree with everyone else: Job well done! You did the best you could under the circumstances, and it pretty much worked out okay (save for one soggy Robby).
Okay, since you asked, what would *I* have done?
Answer: Not worry about it after the fact, that's what. The two of you lived; screw the aircraft that had already violated its "contract" with you. The insurance company will pay for a new one...or not. Could you have turned into the wind? Yes. Could you have done what you did? Obviously. Would either have worked out "better"? Can't say now- but that ship was going in the water no matter what so who care?
Having said that, the accident raises some larger issues. Namely, is it absolutely imperative that there be a helicopter flight school operation at that airport? Aviation is all about managing risks, and perhaps that particular airport is simply too risky a place to be operating a flight school. (Unless, he says tongue-in-cheekily, you put the disclaimer in your brochure, "Students *may* be required to practice actual, unannounced water-ditching procedures.") Let's face it, just because there is a market for something doesn't mean that market must be serviced. Or maybe a Mariner would be a better choice of aircraft. Or maybe you could find a remote site to go practice traffic patterns.
It's not hard to imagine a resulting court case (at least, in the U.S.). You're on the witness stand, up against the aviation-smart lawyer for the deceased plaintiff's family (in this hypothetical case, the student did not make it out of the helicopter safely).
Plaintiff's Attorney: Soooooooo...Mr. Flight Instructor, please tell the court, what exactly happens to a Robinson R-22 helicopter in flight when the power to the main rotor stops.
You: <gulp> "Well, the helicopter descends and lands under full control."
Plaintiff's Attorney: Full control! That's interesting. Please tell the court, in your own words, just how steep and fast that "descent" is.
You: <gulp again> "Well, ah, I would say that it, ahhhhh, comes down like a, ahhhhhhhh, bank safe."
Plaintiff's Attorney: Bank safe?! Are you saying the "descent" would be nearly vertical?
You: "Well...ahhh...maybe not vertical. Maybe sixty...you know...degrees down. Not vertical. Depends on some things..."
Plaintiff's Attorney: So when operating at that airfield, and when turning crosswind at 600 feet in a normal traffic pattern, is there ANY way you can make it back to solid ground in your non-float-equipped helicopter occupied by your non-life-jacket-wearing passenger?
You (weakly): If I could have, I would have.
Plaintiff's Attorney: And you think that this is a prudent, reasonable, and safe manner in which to operate your helicopter? ...Especially with a passenger who...<voice booming now>...COULD NOT SWIM??
Your Attorney (whispered aside to legal assistant): We are so screwed.
Maybe I'm being overly paranoid. Maybe such a scenario would never happen. Maybe I've just been around aviation (and lawyers) for too long. (Chime in, Flying Lawyer. Honestly, how would *you* prosecute such a case?)
Wildwilly, it's silly to beat yourself up over this accident now (although probably every pilot would second-guess his decision for a long time). Even so, it doesn't even do any good when you know full well that the time to be asking the tough questions would have been *before* an accident occurred. "Hey, what happens...you know, REALLY happens when we get out there on downwind and the engine quits? ...And we can't make it back to shore? ...And we have no floats?"
Oh don't be silly, that never happens. Look, you want this job or not? I've got a stack of resumes "this high" from Robbie pilots just like you who want your job. NOW GET OUT THERE AND DO SOME OF THAT PILOT SH*T - that's what I'm paying you for.
Yep! And now you've got an accident on *your* record that you'll have to live with. Be glad the student didn't die. Be glad if the insurance company doesn't come after you for the hull value.
Life's a beach.