As a native New Yorker, I'm one of those who have this "intrusive R" as part of my native speech. Here's my (non-specialist) explanation of the reason we speak the way we do.
First, we drop the R sound in words that end in R when that is the last word in a phrase, or when the word is followed by a consonant. So, for me, "sore" is pronounced the same as "saw" and "lore" the same as "law". So (for example), the expression "sore loser" is pronounced the same as "saw loser."
Second, we do pronounce that R when the following word starts with a vowel. (BTW, this is quite analogous to liaison in French.) So (for example), the R is pronounced in "he's got a sore elbow."
Third, we use the same pattern when the homophone (e.g. "saw" for "sore") is followed by a vowel. So, "He's gotta saw everything" is pronounced just like "he's got a sore everything."
In "law and order", "law" is followed by a vowel, and "order" is the final word in the phrase. So I pronounce it the same as "Lauren oughta." (Not "Laura Norder".)