@Mathrafal unless we somehow end up with ent and elgi besieging us we will always be outnumbered.
And yes they will have to defend from two sides, but we will also have to guard twice the ammount of walls because if they break in one of the entrances we have a big problem.
Making a series of secret entrances would also allow us to attack an enemy in the valley (plus they will not expect something like that unlike with a big entrance), heck with time we should have secret tunnels that lead outside the walls in the passes so that if the walls were to be besiegied by artillery a force could sneak behind.
@Jreengus sure the farmers will always exit the gate evriday, but many dawi could very easly live without ever seeing the sky, the miners will probably only exit to serve in the military, same for the smiths, the stonemason will only exit for project outside the hold, but after we make triple big walls around the for passes there isn't really anything big they have to do outside.
So the only two numerous group of people who will use the entrance after we finish settling ourself in would be the army and the farmer, considering how big the entrance his I would say that we are fitting all of them easly.
we really do not have anybody close enough to trade, and even if we had (Rivendell and the bear people at best) it shouldn't be a big caravan.
Even if we wanted to make another big gate in the southern mountain I suggest we make a tunnel that connects the two peaks first, since we would have to split our forces leaving an escape route should one of the two entrances fall is a must.