My original post about engagement was in response to your 'she knows when I mean it' comment. Does this mean that you now think that you need to be perpetually stern & in an angry mood for her to 'obey' you? If you're interested in dog behaviour & how they learn then do some proper research, but it will bring with it more questions than answers.
Forget all the mumbo-jumbo about 'respect' & 'willing to please'. You need to start thinking in terms of the consequences of behaviours, pleasant or unpleasant, & manipulating those 'consequences', because it is this that will dictate whether a dog is likely to repeat a behaviour or not. As for engaging the dog so it is focussed upon you when under distraction, how you do that depends upon what methodology you train by. I use reward-based methods so I put a lot of work into making engagement with me rewarding, generally through the use of edible rewards for starters. If you rely on compulsion then you would make engagement with the distraction unrewarding, generally through some form of correction/punishment.
As for your breaking problem, you only need to gently restrain the dog on a very short training line
should it look like it might break, not bowl it off its feet or let it get up sufficient moment to break the line. I manage perfectly fine on 3 feet of baler twine. And if you want to follow this approach then the line stays on until you have reliability, which is going to be weeks/months, not a few occasions then take it off.
Naj