This is almost meaningless until the animals/burrows bug is fixed.
Right now if you retreat your civilians to a burrow during a siege or attack, all the war animals follow them and even the ones which are chained up to guard your fortress will refuse to fight the invaders and just die pathetically.
Didn't know this was an issue, shows my noobishness. Excuse my naivety, but the first thought that comes to my mind, as a possible work-around, would be something like this:
Stage One Burrow:
Safe dwarf area chained up dogs (not a part of burrow)
|
v
+--------+
| | x x x
| |
+--------+
______________________________________________________
Stage Two Burrow:
Safe dwarf area chained up dogs area
| -note the lack of- |
v -defined burrow tiles inbetween- v
+--------+ | +---------------+
| | v | x x x |
| | | |
+--------+ +---------------+
Assuming it works like I think it does, you could start an alert for for the first burrow, then when all the dwarves are inside their area, change the alert to the second burrow which includes the dog area. The dwarves shouldn't run to the dogs, since they would have to leave the burrow to do so, while the dogs should be able to focus on fighting since they aren't trying to run back inside the burrow.
It seems you're subject to a common misconception regarding burrows: Burrows define where dorfs may take up "work", but has no effect on pathing to or between work places whatsoever. The path taken is the "shortest" one (as DF calculates it) without regard to whether it passes through non burrow tiles or not. Thus, residents are free to move between disjointed burrow locations, but won't do so unless they have a reason to go to the other one (e.g. to pick up a seed for stockpiling).
Civilian alerts add to the normal alert functionality in that it actually forces civilians to move inside a burrow initially (which work burrows don't: burrow someone in a location with no reason to visit it, and the dorf just stays rooted in place [quite possibly cancellation spamming about not being allowed to drop off something hauled, without dropping it]).
The two burrow system would be safe if the procedure included blocking the path between the burrow segments, e.g. with a drawbridge. If you have an open path and the chained animals kill invaders, burrowed dorfs would run to pick up the corpses and corpse bits (including the dozens of half teeth, each generating its own hauling job, unless you change the corpse/carcass dropping settings).