In the following sentence what is the complete predicate?

Our neighbors across the street are remodelling their kitchen

The complete predicate is "are remodelling their kitchen".

A complete predicate contains the verb and the words that contain more information about the action. In the sentence "[o]ur neighbors across the street are remodelling their kitchen", "are remodelling" is the verb phrase and "their kitchen" is the object that gives more information about the action. To find the complete predicate, you should ask what the subject does.