Extending the Kentico UI field may be a bit out of reach for most, but you can create a Module and add a custom custom ASCX control that has either just a textbox (you can use Kentico's CMS:FormControl to use one of Kentico's URL selectors) and a button that will take a page and go through it's children and order them.
Once you have the child documents, sorted by Event Date, then you can update the NodeOrder of each, or if you wanted use the CMS.DocumentEngine.TreeProvider.MoveNodeDown / MoveNodeUp.
However, other than for how it looks on the page, if you just need to sort events on the actual page, you should do that through the "Order By" Statement (EventDate Desc) on the repeaters.