If the child waypoints all have some common item, it should be possible to filter for those caches from the "Children" tab under filters. However, if you only want to send specific child waypoints from a cache that has multiple child waypoints, i.e. only parking coordinates from a cache that has trail head and other waypoints set as well, that's above my level. If you go to one of the numerous GSAK help forums, perhaps someone might write a RegEx statement for you that would pull out only what you want. There are people on some of the forums with knowledge many orders of magnitude above mine when it comes to that sort of thing.
The flag has nothing to do with whether or not the child waypoint is displayed. It is a means of "flagging" a cache or waypoint for some operation such as a filter. I suggest using the Garmin Export Macro which allows export of child waypoints in various formats. Note that if you use the .ggz file format, the child waypoint(s) must be exported as POIs. If you are loading as .gpx, then they will export as part of the .gpx file.
It's a little embarrassing to admit this but I've not figured out how to use Child waypoints in GSAK.
From the screen capture below, you can see I know how to check the box that I think activates the waypoint, but then I can't figure out to use/see it. Occasionally I'd like to have the parking location in my 64s, but I don't know how.