Docks open when they shouldn't

Perhaps there's a Hotspot associated with the bottom dock causing this. Right click the bottom tabbed dock and select Dock Properties. Click Hotspots... if you have a white arrow on the screen, click it, and change the action in the dropdown list.

The tabbed dock on the bottom opens whenever I open the tabbed dock directly above it.

Maybe posting a screen shot of your set-up will help, I am having a hard time visualizing what you mean by tabbed dock directly above.
The only time a dock opens is when docked to screen edge, if you have another dock (not docked to screen edge) above this it would be open and only need you to select tab you want, which should not open second dock. Unless they are real close and you have a hotspot or mouse over action set for it.
Or do you mean you have two tabbed docks on screen edge one on top of the other.
Either way you may need to move one to another screen edge.

No hotspots present. Here's a couple of screenshots showing the docks separately. (I couldn't catch them open together at the same time.) Does this help any?

Just tested this type of set-up, the only way the dock I did not want to open would open is with mouse over activation set for it and mouse over a tab, which would close the first, the one I wanted open but not close the now open dock. With no mouse over activation set only dock I clicked a tab to open would open. Even with tabs half over lapped only the one clicked opened, and would come to top. In your second pic, closed tab is on top of open dock, open dock should be on top. In both pics you have desktop icons on top of tabs, I can't replicate this.

Thanks for trying. I wish I couldn't replicate -- or originate -- lots of these quirks. I'd never examined the conditions that produce the tab of a closed dock covering a section of an open one. Now I did: it only happens when the open dock was mouse activated. Once I click anywhere on it, the trespassing tab goes behind the open dock. Still, IMHO, an open dock should cover a closed one, know matter how it was opened.

I'd never noticed a desktop icon on top of a tab before. I've moved icons away from tabs now. BTW, I only have desktop icons because my voice recognition program (Dragon NaturallySpeaking 9) can only open programs on the desktop or in the XP programs menu.

Back to the original problem: two docks opening when I place the cursor on just one. I tried moving the docks, but it doesn't matter if they are directing opposite each other. The one on the bottom opens wherever I place it on the bottom. The only thing that works is turning off the mouse activation of the bottom one. It's too bad, because I like that feature, but that's the way it goes.

Thks again for the help.