I don't have Word 2016, but I have a template that uses one large table, one row by 3 columns, each column holding a subordinate table, and they each have different formatting. The first sub-table even has another small table inside of it. At least one of the users also has a mail-merge setup to populate this set of tables, and I've never had an issue with formatting changing. I I should say that none of these tables has a proper caption title. They do have header rows in two cases.

So maybe a larger two-cell table holding your two tables (with invisible borders) would help?

I've had some issues with users deleting the page breaks and paragraph breaks between these tables (they are designated to fit two to one 11 x 17" landscape page), and when that happens, two tables with nothing in between them join together and have to be split.

The OP is referring to setting the title in the Alt Text tab of the table properties. This title can then be used in code to identify the table.

Yes, I was just mentioning my setup didn't use those titles so I wasn't quite sure how they would be affected. But I have had no other issues with tables of differing formats nested within larger tables.