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Can anyone explain the relationship between the 3 types of dog and the clue to 28 across.

Not unless you tell us what the three types of dog are and what the clue to 28 across is.

The overall instructions indicate "Three unclued solutions of 13 letters are of a kind referred to in the clue to the fourth one.
Solutions 1 English setter
Solutions 2 Cocker spaniel
Solutions 3 Scotch terrier

Clue 4 "Correcting say, a canine barking in training gets hard (13)"
Solution 4 appears to be "Straightening"

I can see some vague link to the solutions but would like some more profound explanation.

Presumably you got straightening as an anagram (barking / mad) of "training + gets + h(ard)"

The canine reference is probably to a "stray"

The link "of a kind referred to in the clue" is to the word "canine" in the clue.

You've done all the hard work !!

No I did not get the anagram. Why only part of h(ard)?

Seems to be a very forced link. But thanks for the help

Compilers use a lot of abbreviations:
H(ot)
C(old)
R(ight)
L(eft)

If it's in the dictionary, then they feel free to use it. My current pet hate is, usually in the Telegraph, that "a" is replaced by "per" and vice versa - just because Chambers has "for each or a" as a definition of "per".