Shoot the sow first. Many times I've shot the soe and her piglets will stay or come back and then you pick off the piglets. I shog a sow recently and her piglets came back to her side four times. I took out four of her piglets before the stopped coming back to her side. May sound harsh, but we're talking about an invasive species that does significant damage.
This^^^ I always shoot sows. 10 boars can breed a sow 100 times but she is still only gonna have 6-10 piglets, but one boar can breed 10 sows yielding 60-100 piglets.
That or you could buy them a tv