Well, I've just come off the phone to SIL and nieces. I spoke to both nieces at length and they now understand why they mustn't 'play' with sheep or chase animals. They were both very upset at thought of sheep losing their babies and I'm sure neither will ever chase anything again.
SIL and I had a long chat, it had not occurred to SIL sheep may be pregnant and (like me) she was unaware stress could cause them to miscarry. She said there are never any lambs in that field so thinks they are all male sheep (?) but she did agree to never let kids run amongst them in future. She also agreed not to use Chinese lanterns (we had no idea they can harm cows, so thanks for sharing this info).
SIL insists the right of way is not limited to one footpath as there are several crisscrossing footpaths leading to different walks. She also said she disagrees with people owning countryside as when she was a child apparently no-one followed footpaths, they roamed everywhere and threw themselves flat on ground if they spotted a farmer! I'm not defending SIL (and I don't agree with trespassing at all) I'm just pointing out some people have very different ideas and experiences of countryside. It doesn't mean they will leave gates open, litter or mistreat livestock, I think some people have jumped to rather hysterical conclusions on here! I understand the thread touched some raw nerves.
When I suggested signs, I didn't mean one on every gate. But if there's a popular public walk it would be wise to have a sign at start-point reminding people about extra care around pregnant animals and keeping to paths. Yes in ideal world this would not be needed, and everyone would educate their kids. But how do you force people to educate their kids and read country-code? You can't. There will always be people like my SIL who need signs. I agree most people know sheep have lambs in spring, but I don't think it's common knowledge that they are sensitive to stress and can miscarry.
TBH SIL is still so upset by farmer's outburst she is not sympathetic to farmer at all. She said her younger daughter is now refusing to walk in countryside in case they meet the farmer and dog again! She was already nervous of dogs so
being circled and snarled at (whilst yelled at by farmer) has made this anxiety worse. SIL will not hear of me taking her to that particular farm, but has agreed we'll take them to an open farm next visit to teach them more about respecting animals and building confidence around sheepdogs.
I have written a letter of apology to farmer, apologising for the kids chasing sheep and our reaction to her outburst. I have also included a polite paragraph re her own behaviour and suggested that in future she avoids swearing and shouting abuse at children. Because at end of day, while I understand now why she was furious, I think she handled the situation very badly. Being angry does not give you a right to threaten or intimidate. She didn't explain sheep could be pregnant or miscarry, and at time it seemed she was simply on an aggressive power-trip. I agree a stern telling off was needed, but an explanation for her rage would have helped us all. A stream of furious semi-unintelligable abuse makes people react defensively. SIL is still so angry and upset she is unable to appreciate farmer's point of view and would have remained clueless about pregnant sheep had I not spoken to her.
Re the comments about how would I feel if the field were my back-garden... if I bought a garden with a public right of way through it, and I decided to breed poultry in it, I would not assume everyone has the sense to stick to path. Children are naturally inquisitive and want to touch animals and not all parents are responsible. For my own peace of mind I would either fence off the path or put up a sign asking people to keep to path and not to approach animals. My garden, my animals, my responsibility.