Here goes a second attempt. The logic now is as follows:
AucTeX does not handle frames or window creation, but when user selects TeX-error-overview-setup to be a separate-frame, it uses display-buffer-alist to set up one.
Within the error overview buffer, keys 'n', 'p' and 'j' are used to navigate errors and then to jump to the offending place in the file that originates the error.
The jump to those files is done by attempting to focus on the original window where error overview was invoked, and open a buffer. Instead of assuming that the file is opened in the same window, the new function simply keeps track of that buffer and switches to it, either for display, or also for input focus. I had to explicitely use select-frame-set-input-focus to ensure that this works even when the error overview is opened on a different frame.