A neighbor has a red fox den with 4 pups 100 yards from his back door. He has been entertained and placed a trail cam to watch them.
He also has milk goats, another neighbor has him all excited that the fox will kill the kids when born in a week or two.
Killing them seems to be the solution.
Bur I think he would rather the fox move.

How can we persuade the fox and pups to leave his homestead and or protect the goat kids

Go pee on the den.

Seriously, reds are easy to move. A little hazing at the den site and mama will pack up and move.

Could the entire family be trapped an relocated?
We had a family of coons coming in our barn, and while my brother and I were fine with killing adult coons, we couldn't bring ourselves to shoot babies that just sat there cowering, so we herded all five of them into a live trap, dumped them five or so miles away (still on our property) and then set the trap and the momma coon went in since it smelled like her babies, so we took her down to the place we'd put the babies. It wasn't ideal since the mother was released a day after the babies, but at least they got a fighting chance, and there were tracks later, so they might have found each other.
I don't have any experience with fox trapping, but maybe live trap the little guys and use them as bait to catch the mother?

dont trap them...just go disturb her den and let her see u if possible

We messed with the den and never saw them all day, A neighbor shot the dog. So I wonder if the females already moved them. Set traps last night, Ill check the traps as soon as its light

Old game warden told me to pour a little ammonia in the den hole, she will pack em up