Do the updates need to be made 'live' while the values are adjusting and the 2nd GUI is open, or can they be delayed until it is closed?
They can be delayed until it is closed.
Use a modal dialog or JOptionPane
instead.
Using a modal dialog, whatever code line comes immediately after setting it visible, is blocked from being processed until it is closed. That is where you examine (the return value of the option pane &) the value of the controls you put in the dialog. Note that the idea here is do not extend dialog. Instead just create an instance of one in the main code, create the controls, add them to it, and show it using the main frame as the parent.
Putting 'everything in one class' is not a good design, nor what I am suggesting in general. It is just that there is little cause here for the main GUI not to have references to controls that affect/update it.