My advice is stay out of design mode in VS, it doesn't work very well. In your custom project you could solve it by making a copy of that master page in your custom project with a different namespace and that may solve the designer error but the designer is fairly useless and you should be able to ignore the designer error and only worry if you get build errors.
the dialog master page is used in mojoPortal for pages that inherit from mojoDialogBasePage similar as layout.master is used for pages that inherit from mojoBasePage.
The VS designer in general is not very usefull but is especially not useful in mojoPortal because css is loaded differently at runtime than at design time. ie it requires a runtime context to load the skin files from /Data/Sites/[SiteID]/skinname according to sitesettings.
Hope that helps,