My grandsons, ages 8 and 6, told me their mother hits them on their heads, hard, which sometimes causes them to get headaches, slaps their faces all in the name of discipline. What can I do to convince her this is dangerous. I will talk to my son about it but what else?

If the children are being hurt you have a duty to report this to your local Child Welfare office.

Have a discussion on appropriate punishments---punishments that fit the crime.
Maybe offer to help her write a rewards/punishment chart.

I would not presume that anything a 6 and 8 year old has to say is 100% truthful.

There must be something that you noticed with your grandchildren along the way. Have they had bruising, unexplained marks. Are they sad, acting out, complaining of aches and pains. If she's hitting them on the head, and slapping them all the time as you said, there would be signs, in addition to what they have said.

It is important that you speak with both parents, without the kids present. Tell them upfront what they are telling you, and take it from there.

If they are being abused, and you get that sense, and one or both parents are defending the actions of corporal punishment on their young children, then you do indeed have to report them for the safety of the kids.

If that is how this turns out, then at least you have investigated a bit on your own, and the reactions and reasons/excuses of the parents would paint more of a convincing picture to the authorities.

Either way, that you are informed that something is going on, whether it be true or not, you have an obligation to follow it up in my opinion.

Without knowing what your relationship is with your daughter, I would talk first with your son.