InDesign allows three different character-level orientations: "Right-to-Left" "Left-to-Right" and "Default." The last of these more-or-less means "figure out the proper orientation from the context, including the marked language and the type of glyph." However, the last of these can be a problem, especially when someone who does not care about proper markup will happily key things incorrectly if it looks right onscreen. This is especially the case with numerals and parenthetical LTR text in RTL paragraphs.
So make sure you mark your parenthetical Latin-script stuff as English, and if necessary make character styles to apply to parentheses, and in some cases to the spaces, so that any "Default" settings render correctly in both apps. Some experimentation will be necessary in order to get it to round-trip Close To Perfectly. (It'll never be perfect, I think.)