Where in the telling of this tale did it say they fought about this in front of the kids?

It didn't say either way.

She found out about it when the school called and then she and the ex got into a huge fight over the phone.

The kids. All of them. Were in school. Out of earshot.

Also seems a little severe to rake her over the coals for not wanting responsibility for a child that isn't hers when HIS OWN FAMILY has also washed their hands of him.

Come on. If your family of origin won't support you, clearly there's a whole lot more going on.