I believe you have two different bugs here.
The obscured button thing is new to me. Don't think I've seen that one.
The second bug (resizing) is a known one, ie it was fixed in D2009, but there is a solution.
I found it in a JEDI VCL bug fix report and when I it applied to my code it worked great.
JEDI Issue Tracker Report
The fix can be non trivial for users of the native Delphi VCL docking system. If you're using a third-party docking system such as JvDock from the JEDI VCL it already has it supported. I implemented it in one of my major applications but I'm using a mixture of native VCL docking and third-party components.
I wanted to post you the solution I have but I got looking into my code and it spans a bunch of units and parts of the main code tree.
There is no simple answer except maybe you want to look at the JEDI docking system.
There is also another known bug with DockingTabs under vista, in that the obscured areas of a "docked" window when they slide closed doesn't repaint properly. Slide out works fine, slide in (hide) doesn't there is a solution to this one as well, but it requires modifying VCL source to make it work.
Sorry,
Ryan