She can go to any family gatherings she likes, if she doesn't mind being near him. Personally, I would not sweep it under the carpet and if it were me organising a family gathering and I knew someone had a problem with an abusive person, it would be the abusive person not getting the invite. But I am narrow minded and unforgiving about certain things.
Sitting sharing a meal with someone, drinking with someone, chatting with someone, all very hard to do it you really disapprove of them. For me, it would have long lasting effects to be civil to someone who had hurt children.
OP has said that she believes entirely what SIL has said so I am going on this as being fact. The fact is, he hurts his children.
OP will become part of the 'don't talk about it' lot, the ones who paper over things for the sake of peace. Some can do this, some cannot. If you told me that someone I was in a room with had abused a child, I would leave the room. I would not want to be part of a social group with that person and would certainly not choose to see them again. For others it is enough to just ignore them, although then what do you do if they approach you, make a scene or talk to them? For others, they can be civil. Others can forgive completely.
This is entirely my perspective, the OP has to decide for herself what is important. But I do see it as condoning their behaviour and relationship if you socialise with someone instead of avoiding them. Again, just my opinion.
I reiterate, I am in no way telling the OP what to do, just what I would do. If she feels that she doesn't want her children near him, I don't see how she can go to family occasions where he is there. Maybe if everyone stopped condoning his behaviour, he would not be welcome and she would be free to go where she liked. But until then, she has to choose.