JSFiddle - React, Tailwind, and code Playground

HTML

<script src="//cdn.datatables.net/1.10.2/js/jquery.dataTables.min.js"></script>
<link rel="stylesheet" href="//cdn.datatables.net/1.10.2/css/jquery.dataTables.min.css">
<table id="example1" class="display" cellspacing="0" width="100%">
    <thead>
        <tr>
            <th>Name</th>
            <th></th>
        </tr>
    </thead>
    <tbody>
        <tr>
            <td>a</td>
            <td></td>
        </tr>
        <tr>
            <td>b</td>
            <td></td>
        </tr>
    </tbody>
</table>
<table id="example2" class="display" cellspacing="0" width="100%">
    <thead>
        <tr>
            <th>Name</th>
            <th>link</th>
        </tr>
    </thead>
    <tbody>
        <tr>
            <td>aa</td>
            <td></td>
        </tr>
        <tr>
            <td>bb</td>
            <td></td>
        </tr>
        <tr>
            <td>cc</td>
            <td></td>
        </tr>
    </tbody>
</table>

JavaScript

$(document).ready(function () {
    var a = $("#example1").DataTable({
        "orderClasses": false,
            "columnDefs": [{
            "orderable": false,
                "searchable": false,
                "render": function (data, type, full, meta) {
                return "<div class=\"moveDown\" style='background-color: green;'>move down</div>"
            },
                "targets": [1]
        }]
    });
    var b = $("#example2").DataTable({
        "orderClasses": false,
            "columnDefs": [{
            "orderable": false,
                "searchable": false,
                "render": function (data, type, full, meta) {
                return "<div class=\"moveUp\" style='background-color: red;'>move up</div>"
            },
                "targets": [1]
        }]
    });
    $('.display tbody').on('click', 'div.moveDown', function () {
        var tr = $(this).closest('tr');
        a.row(tr).remove().draw();
        b.row.add(tr).draw();
    });
    $('.display tbody').on('click', 'div.moveUp', function () {
        var tr = $(this).closest('tr');
        b.row(tr).remove().draw();
        a.row.add(tr).draw();
    });

});