You can use heavyweight component (like Panel) inserted directly to JFrame (it will be on top of everything lightweight and also heavyweight if z order is set properly).
I'm adding more concrete howto:
1. create Panel and store content of your dialog there (both AWT and Swing allowed here)
2. call setBounds for your Panel and add it to yourJFrame.getRootPane(), when added into root pane it's not affected by JFrame's layout manager, so you can set positon and size by setBounds
3. create your own JComponent for dialog frame (to which you add real dialog content), which you can use to move around and/or resize the dialog (the JInternalFrame can be probably tweaked to this, but I'm not sure how much work it is)
Don't forget to use reliable source for mouse location, eg. using location relative to parent is a bad choice, even if converted to absolute coordinates as the native events order is undefined and unsynchronized. Use MouseInfo class instead.