Begging, pleading or just asking her to come back WILL NOT WORK. There are many reasons for this. I don't have the time to outline in detail but here is my viewpoint.
Your W has been unhappy with you for a long time (18-24 months at least) she has weighed up her feelings, thoughts and options. That process led her to deciding to leave you and split the family unit. That was not a light hearted decision.She believed it was the best option, maybe even the ONLY option.
Nothing you say will affect that decision except to reinforce it.
To be attractive to someone you need to be a strong independent (or more accurately non- dependant man. You must not NEED her. Neediness,begging and pleading are not attractive.
You should show her that you can live and thrive without her. That is attractive. Aim for that. Fake it until you make it if you need to. Think about what brings a smile to your face or a bounce in your step.Add those things into your life.
Admit it or not but being in a R has restrictions. The benefits of the R usually outweigh those compromises but they exist. Now you have an opportunity to do whatever you want with your life. Live it to the Max. I am not debating the merits of being in a R/M but pointing out that being separated can also be an opportunity. Seize it. Go find yourself and your happiness.
TBH what other choice do you have? None. Either you let this hold you down or you rise above it. A simple choice but hard to impliment.
Going back to your urge. I understand it and I know how you feel. During my journey I have found that every time I had such an urge or felt compelled to do something, most often it was not the best thing to do. If you feel you have to try something or do something, to me that is a warning not to.
I am confident acting on this urge will not bring ye closer to reconciliation but actually further. Again just my opinion. I urge you not to.but if you really need to act on this urge, go for it. Maybe her reaction is what you need to accept where she is and that you cannot change that. Maybe then you will be able to focus on YOU and YOUR goals.
Best wishes
R 25 years M 14 years S11 & S13 Working on it alone since Oct 2014 M in trouble a lot earlier (~2 years) Feb 2016. 1st R chat in a yr. Next R chat Aug'17 Still together