Where were the dwarves in the LOTR?

[badlands]

Did they abandoned the alliance between men and elves?

[Michael]

The Longbeard Dwarves (Durin's Folk) were headquartered in the Lonely Mountain beside the City of Dale at the time of The Lord of the Rings. So to learn what happened to them, you have to read the appendices.

Basically, an army invaded Dale's eastern border and drove the Dalesmen back to their city, and then into Erebor. There they were besieged along with the Dwarves until Sauron fell. At that time, the combined armies of Dale and Erebor charged out and destroyed their enemies.

Gimli later led some of Erebor's people to Rohan to live in the Glittering Caves of Aglarond.