Why tf trees for multi-robot system not showing?

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It seems like you're asking two or three different questions here. I'll provide brief responses, but you should split these into separate questions and ask them again with more details.

(1) when running something (unclear what) in stage, move_base is running but isn't publishing cmd_vel. You've provided a TF tree for this circumstance but no launch files, configs, logs or node graph, so it's hard for me to see anything that indicates why it isn't working. The best advice I can give here is to use rostopic list, rostopic info and rostopic echo on the cmd_vel topics to see which topics move_base is publishing on, what it's publishing, and which topics stage is subscribing to.

(2) your on-robot launch file doesn't work. you've provided the node graph and you say that TF doesn't work, but you haven't provided a tf graph or any of the error messages you might have gotten from running tf view_frames, or any other logs or launch files that might help. I'd advise that you split this into a separate question and include the launch files and the TF error messages that you're getting.

(3) you seem to have some confusion about roslaunch. ROS uses a single ROS master, and multiple instances of roslaunch will all use the same ROS master unless you explicitly change the ROS_MASTER_URI and start a new roscore on a different port.