Answer:

Martin and Eddie, the little fox terrier who is his sidekick, have warmed the hearts of audiences all over the world.

Commentary:

The appositive "the little fox terrier who is his sidekick" refers back to Eddie. However, Eddie already names a specific dog. Therefore, this appositive is non-restrictive and should be set off with commas.

The relative clause "who is his sidekick" refers back to fox terrier. This relative clause, however, does specify which fox terrier is being talked about. Therefore, no commas are needed to set off this relative clause.