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Oh, that's quite a challenge. We don't have any on-the-plate solution to the task but I could give some guidance.
You still allow default column reordering with DataTables. Add a button saying "Save column order". When a user clicks the button you grab DataTables' columns' current order (DataTables api is really great). Then send a request (ajax, post, get, etc) to the server to save that column order for the user.
Later when the user opens the page again you could retrieve the their last saved column order and use it to construct the DataTables accordingly.
Let us know if you need help with any detail. Thanks!