OP I find it really hard to believe that a group of grown adults living in the countryside don't know that chasing sheep is wrong. I'm not a country person but I grew up knowing that chasing farm animals was wrong.
You've said a couple of times that you were concerned, and that you did know it was wrong, so why didn't you tell your SIL that? Why didn't you educate her if you knew?
Especially when she said that the children always do it?
No wonder the farmer shouted, if she has a bunch of clueless adults and children roaming about her land chasing her sheep on a regular basis.
Your SIL and her friends are cowards and liars, prepared to let children take the blame for something they should have stopped them from doing.
And they are idiots for roaming about the countryside completely clueless to the rules they ought to be abiding by.
Just for future reference though, livestock are not toys, and they don't want children to come along and "play" with them. So your SIL really needs to get her "let them play with the sheep" ideas out of her head.
The sheep might be used to being herded, but they're not used to a bunch of clueless people chasing at them, pretending to be dogs (so barking?) and waving sticks at them. They are used to a farmer who knows what she's doing and a trained dog who won't hurt them.
The dog was under control, except it seems to have gotten a bit more growly and snarly as the thread has gone on.
It did not approach or threaten the children in your opening post, but the children were threatening the sheep.
So the father doesn't need to worry about kicking it, although he should perhaps be grateful that the farmer didn't kick his children for attacking her animals, ignorant of the fact or not.
The children heard some bad language and saw a dog. They also heard their own parents lie to the farmer and blame them for everything to get themselves out of trouble.
I know which I think is the most damaging to a child, and it's not the woman who was angry in the defence of her vulnerable and valuable livestock, or her well trained working dog.