Weird. After a quick read, I don't think anyone answered the question.
Men and women pray separately so that men do not get distracted by women while praying.
The basic idea is that men are easily distracted by women - anywhere; any time; any place; all the time!
Or, to put it in apocryphal modern terms - men think about sex every 18 seconds or so...
Men and women who are related do not need to sit separately at the dining table at home.
Men and women who are not related - Do sit separately. Sometimes that's awkward but, it can usually be managed - women sit next women, men next to men, brother and sister next to each other. spouses next to each other, adult woman next to a male child, etc...
In public meals, many Orthodox Jews will not sit with their spouses but at a woman's table or a men's table. At tables where married couples are sitting, most will next sit next to another spouse of the opposite gender.
Does this help?