On your Cousin's profile page, do you see "View Tree" - and if so, what happens when you click on "View Tree"?
Looking at one of my relatives - her ex- does not show on her profile, and she does not show on his profile. Checked another relative - same thing. Checked yet another - still same (ie ex- not shown on profile view).
I typed "Linda Darnell" in the geni search box, and it gave me 107 folks - did you want to provide a link to the one you are talking about, so we can see if we can figure out what might be making the difference?
Still not clear what you mean when you say it doesn't allow you access any more.
If you can see that it does not list your cousin's ex-, then you can see her profile.
-- so, when you are looking at it
1) do you see yourself listed as manager?
2) Below that, do you see "This profile is private." or do you see the Tabs for About, Media, Timeline, etc.?
3) do you see "View Tree"? (sort of upper right on the profile)
As to Linda Darnell - think that mystery is solved - she is a Public Profile, your cousin and the relatives of mine I looked at were all Private - found a Public Relative of mine with an ex- and her profile also lists the ex-. No idea why geni decided to list the ex's on the Public Profiles but not the Private ones - or even if it was on purpose - but it seems like that is how it is working now.
Curious - if you can see "View Tree" on your cousin's profile - what happens when you click it?
Judy Hall and Barry Kessel are listed as each other's ex-spouse on their profile pages, in the Immediate Family list. But they are not shown next to the profile photo. This seems to apply to private profiles.
Lois may be right - in public profiles exs seem to be displayed next to the profile photo. Hard to tell if this holds universally when there are no published specifications.