I believe that XFCE comes with native multiple-monitor support. It sounds like having customizability for both monitors in terms of dock/panel is important, and I'm not completely certain, but XFCE's panels should be completely rearrangeable and separate. They also have decent power in terms of widgets and customizability.

However, KDE and Gnome have more ecosystem features, so if that's important, you might consider that when switching.

Another thing to note is that if you are willing to invest some time, window managers could be the way to go. Most don't have DE features out-of-the-box like KDE, Gnome, or XFCE, so there is a certain ease-of-use gap. But, if you are willing to take the time to get the features you need and learn the environment, window managers work well with multiple monitors. I use AwesomeWM and configure my monitors with ARandR. You can customize your monitors to your heart's content.