Hey
@Alleeluna. OK, so first off, I think you're a bit muddled about the use of the clicker. It's not a distraction or "come to me" signal. It's a signal that "what you're doing right now is what earns you a treat". So that's one really good reason to stop using it in this situation, because if she understands it that way, then you'll be reinforcing the pestering behaviour, making it more likely to happen in the future, rather than stopping it. If she
doesn't yet understand it like that, and thinks of it more as a "come to me" cue, then you have a different set of problems: firstly, you won't be able to use it as intended going forwards and secondly that you're "poisoning" the "come to me" cue by asking her to do it when she's having fun.
So, what to do instead? The first rule in any situation like this is that management is key. When you're not specifically training for something (and we can't all have our training hats on 24/7) you need to ensure that you have your environment set up so that she can't practice the behaviour you don't want. That can look very different for every situation. It could be that Luna is in a play pen when you can't be watching her, or you use doors and/or (sturdy

) baby gates to separate them. Maybe she's tethered to you with a house lead for short times.
That's your first step. The training part is separate to this, but I don't think you should be swamped with too much information at one time. So go away and think about what management techniques could be practical in your situation and write them down here.
Ditch the clicker for now, until we have it clear in your head how it should be used going forwards.
Then we'll come back to training afterwards.
We have your back, and we all
really understand what little gits Labrador puppies can be at times. But we still love them
