Legal Question in Family Law in New Mexico

You don't give me a clear picture of your custody arrangement: do you have an order from a court (parenting plan or other order), following a divorce, giving you physical custody? She can always ask for a change of custody based on a change of circumstqances, the burden of proof would be on her. Kids age 13 and up can have input to the judge's decision, but the judge is not bound by their wishes.

You don't need court permission to do a DNA test on your kids if you have custody, but you may not really want to know the answer. In principle you could use the results to show you are not the biological father and try to disclaim responsibility for future child support if she got custody but you would be entering a gray area of the law. There is a presumption of paternity if you are married to her when the child was conceived. But do you want to give up custody? Do you have a solid parental rfelationshiup with the kids? Do they want to leave?

You have never denied paternity, apparently, and so have effectively claimed it and may have waived your right to deny it. It's not real clear to me whether a court would allow you to disclaim it at this point. DNA tests are admissible but not binding on the court. To work that issue you need to really get together with a lawyer (and bring a lot of money).

I've read some studies that claim that somewhere in the neighborhood of 10% of children born in marriage were not fathered by the husband. In these days with DNA testing it is possible to know that for sure, but if you have a good relationship with your kids why would you want to plant that barrier between you? That's why I said, you may not want to know the answer. Also consider that she may just be gaming you with the claim that they're not yours. If she has shown herself to be unfit before and you have custody on that basis, then without some miraculous change in her character she is not likely to get custody. Maybe you could work out informally some increased visitation or something that would not amount to a change of custody, and get her off this kick. Good luck.