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A work colleague has recently taken on an ex-racer and it's been really enlightening as to their quirks, they're simply not treated the same as a pet dog during their careers and may take a while to adjust.
'Ere are you calling the Greyhound Gang quirky?
You sound to be really sensible OP and are taking the right approach, as BC has said it might be worth going back to the vets to check out possible incontinence but personally I might be inclined to see how the 'house training' goes first. Good luck, hope all goes well