Quote by jellybelly
My solution got custody of my children soon shuts them up !!!!!
Can't speak from experience (as myself and Mrs TnH are lucky enough to be together) and hope to never go through this. However I have helped a few friends caught in this trap. I also have family where the husband went for custody and won, he has been a great father from there on. Without to my knowledge any financial help from ex wife.
From the sounds of your post she is taking you for a ride, I would say document everything, quietly. Keep your swinging very quiet, it will not help you in court if they start digging for dirt. (Not that I think swinging is dirty, but don't give em ammo). See what you can do in medium term on custody as per Jellybelly's advice.
I know there is no easy solution here, join fathers for justice and see if they can offer better advice. It is unfair of her to have you worried she will withold your access rights to blackmail you for more money.
Wishing you both all the best babes.
TnH