Need help resolving two compatibility issues that have reared up with IE 11 and DNN 7.2.2;

The first happens only for some users - when the login it accepts their username/password and reports no errors, but then when the page refreshes they are not logged in. The site event log shows that the login was successful (so they did enter their credentials properly) but the login doesn't seem to complete.  Same user can login fine with Safari, Chrome, and Firefox - just not IE 11.

The second is that we have a child site setup. when a user is logged into the parent site parent.com and then tries to open a new window to a page on the child site child.parent.com IE hangs and then eventually gives up. Doesn't matter if the child site is manually navigated to or opened via URL.  However, if the user logs out of the parent site, then opening the child site works just fine (again, regardless of how the page is opened).  And, just like the first problem, it can't be reproduced in any other browser except IE.

Ideas? Anyone else have this happen? 

clearing browser cache was first thing I had the user try.  no change.

Yes, it happens on ALL child pages.  I should also note that ALL the child pages being accessed (including the home page)  have no restrictions - permission set for ALL Users to View.  So there "shouldn't" be a security issue.  Also the child site event logs do not indicate any errors or that anyone is trying to authenticate.  no errors at all.  as the site is simply not being accessed...