Hello,
UPDATE:
Prevent break tables using addTable
Prevent break tables using HTML
MS Word doesn't include an option to keep tables on single pages (https://word.tips.net/T000865_Keeping_Table_Rows_Together.html). You can get a similar behavior using keep lines (page-break-after: avoid;) and keep next (page-break-inline: avoid;) styles, but they are only available for paragraphs. So you should add paragraphs for each cell and then apply these keep styles.
DOCXPath and DOCXCustomizer can be helpful in modifying tables an applying that kind of styles after the HTML to DOCX conversion has been completed, but they are only available in Advanced (DOCXPath) and Premium (DOCPath and DOCXCustomizer) licenses.
About your question, sorry but there's no way to force a text-align to cells within table inside another table.
Regards.