Currently, to have any type of inset, it must be it's own independant data frame.
Instead, how about "sub-frames" where the data is still connected, you are just viewing a different area/extent.
Example: Map of USA, to include Alaska and Hawaii you make seperate data frames with independant symbology, so a change to one symbology requires going in and changing sybology for all 3, or more, data frames.
Instead: Use the "sub-frames" to bring the other two states into view, with connected symbology and lables and only one layer of annotation that goes over top of it all.