I think whether or not clicking and treating for looking at a trigger will be effective will depend heavily on why she is reactive (ie, the underlying emotional state that is causing the problem behavior) as well as what the end goal is (ie, what you you want her to be doing instead of reacting?). IMO, this approach is going to work best with a dog where the problem behavior is distance seeking behavior, meaning that the dog is reacting in an attempt to make the trigger go away. Usually this is motivated by fear or anxiety, and it is a fight response to what the dog sees as a threat to itself and/or its people. This method does a great job of turning noticing/seeing the trigger into a predictor for getting a treat.
So: do you know
why she is reacting? Is it fear or anxiety, is she frustrated and wants to go greet the dog, is she over stimulated and expressing that by vocalizing/lunging/etc? Did the trainer you worked with have any insight on why she was doing this, and what did the trainer you worked with suggest (and also- did that trainer actually seem like they knew what they were doing)? Also, out of curiosity- how old is this puppy and what is her background?
Most of my advice is going to depend on why she is reacting. I'm going to focus on it being from fear/anxiety or from frustration in my response, simply because IME those are the two most common reasons for reactive behavior.
Personally, I am not a huge fan of this approach as the sole behavioral modification tool being used because it is focusing more on changing the emotional response to the trigger than it is focusing on teaching an alternative behavior. Depending on why the reactivity is being presented, you might be setting yourself up for escalation or retarding progress. When I give on-line advice about behavioral modification, I think it is really important to be giving equal focus to changing the emotional reaction to the trigger AND teaching/reinforcing a more desirable, alternative behavior/way of interacting with the trigger simply because there's no way for me to know 100% why the dog is doing what it is doing, and which I stress working the dog in person would depend heavily on why I felt it was behaving that way. Truthfully, that is why I am so quick to say "find a professional to work with in person." It sounds like you're sort of needing to fly this blind and do this yourself, though, so I won't give you that tagline and instead focus more on giving actual advice/resources.
If this is reactivity caused by fear/anxiety, that isn't necessarily the worst thing ever, because in that case I would want to be focusing on the emotional state before I was focusing on the desirable behaviors being offered. If this is reactivity caused by frustration, I would be focusing on teaching the desirable behaviors first and then letting the emotional response to doing those behaviors and being rewarded for them bleed into the underlying emotions.
Since this approach is focusing mainly on changing the emotional reaction to the trigger (I suppose that looking at the trigger quietly could be considered a behavior, but if this is NOT from fear/anxiety IMO that's not a useful behavior to be encouraging), IMO depending on the root emotional cause of the reactivity, it is very easy to escalate the reactivity if the trigger is continuing to approach closer and closer and then eventually under your dog's threshold distance. The positive emotional response caused by the treats is going to be over ruled by the building stress of the approaching trigger. Really I'm not a fan of working under threshold distance at all if I can help it; I prefer threshold distance to be something that lowers naturally as the dog's emotional response to the trigger changes.
If a dog is under her threshold distance, IMO that is a management situation more than a training one. The best thing you can do is take her attention off that trigger and put it onto you (ask for behavior that conflicts with her reacting and keeps her line of sight directed away from the trigger- it has to be very solid behavior that has been strongly reinforced and learned absent of triggers, though) and try to move away from the trigger. If you absolutely cannot move away from the trigger, then try your best to distract her from it. I really do not recommend using walking paths for this reason- you can't get away; once the trigger is coming at you, it's going to pass you at some point and it's likely going to pass you fairly close. Parks are great places to train, but stick to more open areas where you have space to maneuver, and plot out line-of-sight breaks in the park should you need to break her line of sight to get her to stop reacting (this can help in management situations where a trigger surprises you and you want to get above threshold distance; the line of sight break can be the different between moving 20' away and 10').
I would recommend keeping some very smelly, very high value treats in your treat bag AT ALL TIMES (even on normal walks that you aren't planning to do formal behavioral modification on). Scent is a very powerful thing. It is able to break through the over-focus that most reactive dogs get on a trigger above threshold distance where physical sensation, noise, and visual stimulation does not. When you are in a situation where the trigger is above threshold distance, stick a smelly treat in front of her nose. Unless you are WAY above threshold with her, this should be enough to get her to re-focus on the smelly thing. Then, lure her head away from the trigger and keep up a steady stream of treats for looking away until the thing has passed. If you have to lure her attention away with a smelly treat every time, that's OK. Hot dog, Pepperoni, and Liver treats are all good for this.
Other methods to look into for behavioral modification are:
"Open Bar/Closed Bar"--> again, good for changing the emotional reaction more than reinforcing a different behavior since it isn't looking for a specific behavior. The dog sees the trigger and then gets steady treats until the trigger is gone from sight, no matter what they are doing.
"Look At That"--> mostly used to change the emotional reaction, but does simultaneously teach the dog to look at and then disengage from the trigger to look back at you, first on cue and then eventually becomes a knee-jerk reaction to the trigger. I like this for changing negative (fear, anxiety) emotions more than changing emotions like frustration, personally, though I do use a modified version with my excited/frustrated reactive dog that focuses on the disengaging from the trigger park of it.
"B. A. T"--> "behavioral adjustment training" is very, very cool. My understanding of it (I just started delving more deeply into it) is that it focuses more on 'functional reinforcers', or normal life rewards, to reinforce alternative behavior. Its really good for dogs who are seeking distance from the trigger, because it's teaching them to do the behavior the handler wants to see (usually some kind of calm, healthy, normal behavior and sometimes even involving cued calming signals) and then reinforcing that behavior by allowing the dog to move further away. Grisha Stewert (the trainer who created the protocol) has both a book and some videos about it, which I have heard good things about and am actually just about to read myself.
Good books that talk about how to deal with reactivity by focusing on reinforcing what you do want vs punishing what you don't off the top of my head are "Control Unleashed" (can't remember the author) as well as "Fight!" (by Jean Donaldson). I'd also highly recommend Stewert's BAT 2.0 book and videos. McConnel also has some good books and videos.
McConnel has a lot of good stuff on her blog, as well:
Barking & growling, signs that trouble is brewing | Trisha McConnell | McConnell Publishing Inc.
I'll wait for a response from you before I dump anything else on you, LOL.