Sounds like a bug but it is obscure enough that it may never be corrected. I presume that the floating table's anchor is located in the left side non-floating table so Word gets confused by this. On normal floating graphics you can set an option to see where the anchor is and drag it to another location. Tables don't display this anchor so you need to guess where it might be.

In my experience it doesn't sound like a page layout that I would recommend. Floating tables is not good at the best of times but placing it beside another table is asking for problems.

Can the same visual layout exist by doing this as a single table with a non bordered column between the 'tables'?
Another possibility is to throw in two continuous section breaks and put both tables inline in a two column section.
Another possibility is to live with the same table title and find the one that is floating.

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Andrew Lockton
Chrysalis Design, Melbourne Australia