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You need to remap the /cmd_vel topic in your launch file for nav2 to publish to the topic you want. Relevant snippet from this answer: how-to-remap-topic-in-a-ros2-launch-file

forward_turtlesim_commands_to_second_turtlesim_node = Node(
    package='turtlesim',
    executable='mimic',
    name='mimic',
    remappings=[
        ('/input/pose', '/turtlesim1/turtle1/pose'),
        ('/output/cmd_vel', '/turtlesim2/turtle1/cmd_vel'),
    ]
)

The node to republish a topic to a different topic already exists in the topic_tools package, the relay node there specifically, but as I said, in this case you would just want to remap the topic that nav2 outputs.