The civ screen indications show what the relations are between the highlighted civ and the others on that list. Highlighting dwarves thus shows there's a War relation between dwarves and goblins, while highlighting goblins shows there's a War relation between goblins and dwarves. You can never be at war with your parent civ (maybe in the future...).
Thus, failure to get dwarven caravans is caused by other reasons, possibly goblins besieging the mountainhome. Also, if you get besieged by goblins (or undead) when caravans are due, they'll pass you by. Another reason for caravans to pass you by is that you don't have any path to the trade depot, but a message is produced saying that.
Migrants normally don't arrive during winter, and if you're besieged while they're due to arrive they won't come (which can cause them to show up during winter instead).
Also note that there are two pop caps, one that stops immigration, and one that stops births as well.
Migrants are attracted by fortress wealth and scared away by fortress death, so a poor fortress that suffers serious losses to invaders can have trouble attracting migrants. However, in that case there's a message saying something like "Your fortress didn't attract any migrants this season" when they'd normally have appeared.
There are a number of reasons for why the dwarven caravan fails to show up (including a couple of nasty bugs), but usually they'll appear again as if nothing had happened one or several years later.