Larry,
You have formulated your question very well - I think we need to do a better job of addressing exactly this scenario in our help files as I think it is quite common.
Wild Apricot widgets are basically the same pages as available for people on your Wild Apricot site, minus the header, footer and menu. Thus, each Wild Apricot widget corresponds to a particular function - because it does not have a menu, it can not by itself be used by people to go ton another function. So here is a way I think you can achieve what you have described:
Let's assume that you want to provide access to the secure directory and to their own profile editing.
Create 3 pages on your existing website:
1) member services area. This will provide basic introduction about online services and links to 2) and 3)
2) Member directory. Embed Wild Apricot directory widget in it. (assuming that your directory is stored in a member-only section in Wild Apricot site)
3) Personal profile - embed Wild Apricot member profile widget.
Now people can start at page 1) or go directly to 2) or 3). In either case they will be asked to log in before seeing Wild Apricot functions. They will stay on your main website.
I hope this helps, let us know.
See also http://help.wildapricot.com/display/DOC/Widgets+-+integrating+Wild+Apricot+into+another+website
Dmitry Buterin, Chief Apricot