Meredith, the rules that I explained are "hard and fast rules" in American English. There are definitely some major differences in the use of relative pronouns between American and British usage. As you say, in either usage, the commas are what tell the reader if a clause is essential or non-essential. The "essential-ness" of a clause is definitely in the eye of the writer as you show with your two variations about the mare. Context is often what should tell the writer whether or not to use an essential or a non-essential clause. I would add that for writers who are struggling with the decision that they should consider whether or not the information in the clause is necessary to convey the "essential" meaning of the sentence. If it's just an extra, interesting side note, the clause is non-essential and needs commas and "which" or "who" in the US. If the information is necessary to convey your meaning, then use "that" or "who" (and you may use "that" for people in the US) and no commas.
Schoolmarm
