Sounds like you are taking very good steps to protect you and your son.
50/50 custody is solid. Well-done.
See a lawyer for your own peace of mind. Make sure he/she protects your interests, but don't let them drag you in a battle. If your separation plan is good for you, make sure that sticks for the divorce.
Worst-case scenario: you desperately cling to your wife and lose custody of your son. You just avoided that. Thank goodness!!!
Best-case scenario 1: you live a great life, move forward in separation/divorce, love your son well, and get you mojo on. Your soon to be ex-wife notices, has a change of heart, experiences deep remorse and does the real work, which opens the door for reconciliation. Your marriage is back together. Bravo!
Best-case scenario 2: you live a great life, move forward in separation/divorce, love your son well, and get you mojo on. Your ex-wife doesn't care and moves on with OM #1, OM #2, etc. You have just dodged a bullet. Your flaming turd of a wife is now someone else's problem. You fill your life with people worthy of your time, who are loving and loyal. Your son has at least one sane parent, and you will find love again. Bravo!
Same action plan for both best-case scenarios. The only thing, I think, that can re-attract your wife is the sense that she's losing you and that she's close to crossing a line of no-return.
Pleading, begging, being nice will only solidify her sense of disdain for you and her entitlement. You don't have to be superman and super-husband (the husband only a fool would leave) to re-attract your wife. You just need to show some spine and resolve. If that doesn't work, then good riddance.