Voluntary change of custody

Specifics:
Ex lives in Lincoln County, with 3 kids.
I live in Wake County
We are officially divorced. We have joint custody of the 3 children, she has primary physical custody, I see them every other weekend, alternating holidays, and a month in the summer. The custody agreement was filed in Lincoln county.

My question is: She sporadically throws up when we disagree “you take them then. I would love to be rid of the obligation” (I know… wonderful mothering instincts are her speciality). Well, up until recently that was always a hollow phrase because it wasn’t possible due to work, finances, etc. But now it just might be possible. But, she is adept at changing her mind, which she would, when the child support stopped. So…

1)Can we, if we both agree, just have me take the kids and have them live with me?
2)If so, is there a way that I can prevent her from simply changing her mind once again, slapping me with the original court filed custody agreement, and taking the kids away with the law on her side?
3)Would I need to do anything legal-wise, and if so, where would I file, Wake county or Lincoln county?

Thanks for any clarification you can give.

You may change custody, and should amend the agreement by filing a new one with the court which outlines the new terms. It should be filed in Lincoln County.