2

In The Parent Trap (1998), pet dog never recognize Annie (acting as Hallie) as Hallie and thinks as strangers. Even Chessy (working for Nick) thinks Annie as Hallie.

Actually, Annie and Hallie are twins and switch their places at school picnic after realizing they have the same parents, then Annie goes to Nick (Father) as Hallie & Hallie goes to Elizabeth (her mother) as Annie.

Actually, Pet Dog belongs to Nick.

I already saw this question, but it doesn't mention about twins in humans.

3

Yes and no, it depends on dog's training.

From livescience.com:

Research investigating whether dogs can distinguish identical twins from one another has gone on for more than a half-century. However, the findings of these studies have proven conflicting and inconclusive over the years.

Scientists in the Czech Republic suggested any discrepancies seen between the results of past experiments might have been due to different levels of training of the dogs used in each. Instead, they suggested using police dogs with the highest level of training, noting that such canines have been used in police lineups to identify people by scent in Europe and the United States.

Researchers started with samples swabbed from the bellies of two sets of identical twins, boys age 5 and girls age 7, as well as two pairs of fraternal twins, 8-year-old girls and 13-year-old boys. Experiments with 10 German shepherds then had each dog go through 12 tests, all of which involved the canines sniffing a swab and then seeking out a matching scent from seven possibilities.

The scientists found all the dogs picked out the correct match every time. They distinguished identical twins from one another without fail, even though each twin lived in the same place and ate the same food as their counterpart. In comparison, DNA tests could not tell identical twins apart, although they could naturally tell fraternal twins apart, which are only as genetically similar as any regular pair of siblings.

"Dogs can discriminate the odor of identical twins if well-trained," said researcher Lud?k Bartoš, an ethologist at the Czech University of Life Sciences in Prague.

So in short, Dogs can distinguish identical twins but it depends on there training and intelligence level.

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