Rotate a Widget?

I'd like to have alternating (rotating) widgets in one location on my sidebar. I've looked at tons of plugins and done many Google searches, and am not finding what I want. I don't find that this has been discussed on this forum, either (if it has and I missed it, please excuse me). I'm wondering if anyone knows of a plugin or specific code I can use.

The contents of the widgets are just HTML, but I want them styled just like all the other widgets. When I tried using Ad Rotator, the styling was off -- specifically, the font sizes, even after adding a CSS insert. If I could get the styling fixed with Ad Rotator, it would do what I want . . . I think.

I don't want to use a tabbed widget (I have those in other locations) -- I simply want a widget that changes each time a page is loaded.

If you look at my site (http://theboatgalley.com), note the second widget on the right -- "It's Hot Out!!" I want to create a couple other similar widgets to draw attention to highly relevant posts (which are really lists of relevant evergreen articles) about other topics. I want it to change each time the page is loaded for times, such as right now, when there's more than one thing I'd like to highlight right there at the top of the sidebar.

My ideas:

A plugin that's actually designed to do this. OR

Use Ad Rotator and somehow get the styling right. OR

I have a widget that can accept PHP so I could code a widget area to randomly call or rotate the widgets if I had a clue of what that code would be.

If anyone has a clue how to do any of these or has a better idea, I'd love to hear it!

Thanks!

Carolyn