I get shining products from my livestock all the time but I'm also working on the last bell (fall 1st yr).
*spoiler* after I ran the green bell, the one on Horn Farm in the windmill, they all commet that the animals are happier now so it might be connected to your issue. I don't recall getting shining stuff before I ran the green bell.
Yea, ringing the bells are the key to shining products. Milling, too - since power of the wind is in one of bells
Also, for milling, weather does affect watermill - some products loose as much as 2 ranks on rainy day. Best time to use watermill is blizzard in winter (+2 in ranks), or just regular sunny non-windy day (same ranks)
Animals don't give shining products until you ring the green bell I believe. I thought this was just luck on my end, but hearing you talk I'm now pretty confident that this is how it works. As for the watermill.. I thought the blue bell let you get shining there, but maybe the green bell is responsible for all milling, not just the windmill. Or maybe you haven't gotten the scene with toby talking about the rivers being alive again or something.