As documented in this help topic, you cannot remove or reorder the default buttons. That is why we show them in gray:
The reason why the mirror button does not show is that only available commands (non-grayed out) are shown in the Context Toolbar when the toolbar comes up. In this case, it looks like you have added the mirror assembly command to the context toolbar, but it looks like you are probably in a weldment part, not an assembly, hence why the assembly command is not available.
I hope this helps,
Yes, it does help. Thank you very much!