Schedule Tasks - "Do" Dates vs "Due" Dates

It would be very helpful to have a drag and drop scheduler where you can move tasks around for when you PLAN to do them, without it changing the actual due date. Many project management software help us manage everything that needs to be done, but they're lacking in the ability for us to actually SCHEDULE the work to be done (as they are reliant on due dates instead.) Nobody wants to work on a task the day it is actually due, way too stressful lol. Bonus would be if when on the scheduler a task is going to be overdue based on the date you plan to do it, that it becomes highlighted in some way so you know it is past due. And a side column to list all tasks that you don't actually have scheduled "to do" yet. Would be so helpful in planning schedules.