You can place 2 pics side by side by aligning both of them left. You will have to adjust the left margin of the left picture (in the advanced settings) so that the pair looks more centered.
After the pair of pictures, you insert this code in the Text Editor so that subsequent text does not wrap to the right of your pictures.
Your code shows that you used align none for two of them, then added an "aligncenter" probably by using the formatting tool to center text in the visual editor. That seemed to work too. But I'm not sure that is the real way to do it???? I just don't know.
Dream Weaver is software to design a whole website. It won't help and can't be used here on WordPress.com.
Windows LiveWriter is free. But can't be used on a Mac. Lots of other volunteers here have recommended it though. You can do all of your posts offline plus save them to your computer with it. There are offline editors for Macs, but I'm happy enough with working directly online and the last time I looked, none of them will write tables.
There are free "table generators" online, but they are not necessarily using the latest versions of code…
I'd say try the procedure of inserting captions last as I described above.
If that doesn't work I could show you a basic table code for you to fill in. The problem is that some themes add extra styling and I'm not familiar with your theme to know what you'd want to change. Things like color, font, spacing, borders, and so on.
Here is a basic table code for 2 rows and 2 columns:
<td>CONTENT ROW 1 CELL A</td>
<td>CONTENT ROW 1 CELL B</td>
<td>CONTENT ROW 2 CELL A</td>
<td>CONTENT ROW 2 CELL B</td>