Hiya blackthorn,
I'm sure someone here will have a better idea of what you may need to do since I don't use the VSD program at all. I just wanted to make sure you are aware that you cannot edit these files in the HTML editor and then back to VSD. VSD won't allow you to import any changes made outside of the program, so if you're planning to do any other editing of this site within VSD then you should work out the issue within VSD. If not then you're ok to go into the HTML Editor without issues.
Having said that, the HTML Editor is a code setup rather than the visual setup that you have with VSD, and I would STRONGLY suggest you don't use the visual editor in the HTML Editor with your VSD site pages as it will definitely mess up the code on you if you swap it back and forth.
And having said that, to edit the tables you'll need to edit the code itself. If you can supply a link or the part of the code that you want to alter (paste it into the forums here) I'm betting someone can help you very quickly. Hard to know exactly what to tell you to do when we don't see the actual page or code. Someone that uses VSD may know offhand though. The reason of course is the code is extremely different between the 2 programs, and if the tables are written as differently as much of the other code is, that could be why it's giving you issues trying to "insert" things. Not sure there, but seems like a viable possibility. I'm no help without seeing things unfortunately, as I don't know how VSD writes it's code for tables. Someday I'll play with that program some just so I can help with it better lol.
Good luck on it, post us something to go by and I'm sure someone will be around to give some guidance on it