Will Amaterasu go along with the summoned animal or disappear? Let's say that some summoned animal is being hit by Amaterasu and the summoning is canceled so that the animal can return to its original dimension. 

Will the Amaterasu fire go with the animal to the other dimension and kill it or will the animal be able to escape it by going to its dimension?
The flames of the Amaterasu are inextinguishable by ordinary means and once any organism is caught in it, they will either have to sacrifice that body part, absorb the  entire Jutsu (if they posses Rinnengan related abilities), or seal the flames away.

In the case of a Snake summon, it could most definitely shed its skin and easily escape the flames of the Amaterasu (which would still be burning the outer skin that it shed). This is evident in the fact that Sasuke was able to escape Itachi's Amaterasu by shedding his skin (a unique ability that he learned from Orochimaru, and Orochimaru learned it in Ryuchi Cave ).

A slug summon like Katsuyu could survive but the damage will be immense, since she's able to rearrange her entire body into smaller slugs, she could detach out the parts that are consumed by the Amaterasu, by turning into a ton of smaller slugs and sacrifice those parts. 

Also, If the animal was summoned by a person who posseses the Rinnengan, the summoner could easily absorb the chakra and remove the flames.

As for all other Summoning animals, Unless they have a unique defensive ability to escape the flames, then the Amaterasu will burn it out from existence. Even if the Animal tries to go back to its main habitat, the flames will still continue until nothing exists.