I'm fairly certain that 我今年会见你的家人 works, just reported it

Hey Im a native Chinese speaker and i can confirm that your translation works perfectly.

Is there significance to the different ordering?

Yes it is supposed to be fine

会 got many meanings, say, "intend to", "about to", "willing to".

In this case, it means 'will'

Means "will do" something or "can" do something... like in 我会说英语。which means "I can speak English"

Hui "会" means will