Thank you tansael for this feedback, I am happy you mention it.
Indeed DirectEdit has a very strict validation engine. Basically it removes formatting that is not available in the toolbar. This makes sense when a designer creates the website, and others manage the content – which is the original situation I created DirectEdit for. The validator is one of the ways in which DirectEdit protects a clean design and markup (see https://directedit.co/).
However, I do understand it is not a desirable feature when you do in-content styling with columns and tables. In the next update I will disable the validator by default, and add an option in the backend to enable it if you wish. That solves your problem only partly, because the DirectEdit toolbar does not support tables and other advanced styling yet, but at least it will not break the styling that is already there.
The way DirectEdit might be of use for you is when you create your own template, with the different columns as independently editable elements. So you can create the design of your website in the template, and then add editable fields where you want to have editable content.
Another solution is, if your website only has one or two pages that contain tables, it might be a solution to disable frontend editing for these pages only, which can be done in the backend page editor.
Cheers!