If a Petitioner doesn't respond to the Motions served by Respondent in a divorce case? What happens?

Then the motions can be granted.

You go to the hearings, and request that the judge grant the motions, normally you will win because they have not responded.

Depending on what kind of Motions. The Judge may issue an order to compel or just grant the motions at a hearing. There must be a hearing though as Judges just don't grant motions and issue orders without hearings being held.

What kind of Motions are you asking about?