Dog aggresion a people risk?

Question
We have 2 dogs, a brother and sister(both neutered), ~3 years old.  Most of their lives were spent at my new wife's parents place, just hanging around, doing as they pleased, when they pleased.  This included many instances of them tag-teaming together and killing everything from cats, rabbits, squirrels, chickens, birds, rats, and snakes.  They are mutts, 60 lb mutts at that, and they seem to love to kill other things out of FUN.  

Now that we are married, the dogs have come to my house.  Historically these dogs can get out of any fenced yard over time, seemingly out of fun.  The female is clearly the smartest and the leader, the brother just kind of follows, but is the bigger and stronger.  The female doesn't seem to really care about other dogs, she is more shy and reserved around them . . . but the male gets all excited, all looks and appearances suggest play . . . but will attack them.  He is wagging his tail, no growling or aggression, he appears to ENJOY attacking them.  I really believe that he thinks he is playing . . . but then the animals die, and he's over it.  As soon as the animal is dead, they leave the carcass, occasionally playing with it some more.  Much like a cat with a dead or dying mouse.  So our male has attacked 2 small dogs thus far, injuring both of them severely.  My intervention is what prevented their death.


So, the big question I need answered here is: The neighbors, whose dog was aggressively thrashed in front of their own house, fear for their children from our male dog.  What is the risk to kids if our dog loves to kill animals?  Our dogs are COMPLETELY friendly, tail-waggin dogs when it comes to people.  They never growl, they have never bitten a person.  In fact, they usually don't really seem to care that other people are even around.  If they are on a leash, they are more excited to smell a bush then to smell a person that has come up to talk.  I play rough with them and they never bite or nip.  When I wrestle with them, they don't ever attack back in any manner . . . not even playfully.  They just submit and lay there rolling around.  So, they have never shown aggression to a human before, but they have ALWAYS enjoyed killing other animals.  The neighbor's concern is a legitimate one, because he is concerned that despite our dog's love for humans, our dog may accidentally attack his kids when they are carrying their small dog.  Our yard is fenced, but they escape every now and again when we are gone, thus the incidents.  A better fence could be in order, but even with a 10 foot concrete prison wall, my concern is whether or not our male dog could attack a kid or a human with this kind of aggression.  Again, aggression that seems to be "fun" for the dog, not agro, protect-my-property type.  Because to me, this is the problem, not whether I can get a good enough fence.  Another negative thing is that there is nowhere good to "socialize" the dog.  We live in Mexico right now, and 99% of dogs are supposed to protect property and that is what they do.  So, it is clear that our dogs suffer from UNDERSTANDING that they are not allowed to attack, but there has never really been an opportunity to teach them not to . . . it has always been arriving home to a dead squirrel, a dead rabbit, or the neighbor with his vet bill.  

Thanks a million for any help.  If I have to put the dog to sleep, I will.  We love him . . . but if he is a risk to attack someone's kids, then there is no reason good enough to keep him alive.  

Best,

Peter

Answer
Peter since we are dealing with a potentially dangerous behavior here I would not be doing any favors buy making a recommendation without formal, in person, evaluation of these dogs.  I can however point out some facts that may help you decide.
First lets talk about the fence situation.  You can easily stop the escape of these dogs by installing an electronic containment system attached to your existing fence.  It will cost less than $300 for the two dogs and I would be happy to assist you in choosing the correct one and pointers on installing such a system.
The situation of the dogs killing every little animal they come in contact with is one initiated by their instinct and fueled by owner ignorance.  Since it has become a habit for the dogs to do so and that habit has been accepted, or at least tolerated, by their human owners the dogs will continue it until behavior extinction occurs.  This behavior is more addressed towards the "size" and disposition of the prey than it is the "species".  Your neighbor is 100% correct in fearing it could happen with children.  If presented with the right set of trigger reflexes the dogs could attack and even kill a smaller child.  It has happened hundreds of times with dog less demonstrative and more loving than yours.  For example if a small child becomes scared and runs away screaming the dogs could very well give chase.  (Or if they are trying to protect a smaller animal.)  Once in the chase mode instinct, that has been allowed to grow unchecked during their life, will take over.  Add to that the "pack" instinct when there is more than one dog attacking prey and you have the aggression multiplying even more.  This covers some of the more prominent factors but still not all of them.  I am not saying this will happen but all the ingredients are there.  
You seem to want to some how excuse their behavior by saying in Mexico it is acceptable.  If a dog kills anything  you don't want it too then it should be unacceptable to you.  A dog, large or small, is a predator and whether playing or fighting for its life it can and will kill given the triggering circumstances.  As owners it is our job to extinguish the demonstration of any behavior we do not find acceptable.  
Since your dogs seem to be focused on small animals you should be able to easily socialize the dog to accept and live with these animals.  It is a good sign that you dog reacts to people the way you say and is accepting of all your manipulation.  This tells me that these dogs should be fairly easy to "fix"  You can use small rodents such as rats (they should be cheap and easy to find) to teach the dogs how to accept and deal with the company of such.  I won't go into the exact process here unless you recontact me and ask for it.
Here is my summation of your situation and how I would deal with it.

1. DO NOT DESTROY YOUR DOG!!!  If you do not want to deal with it find someone who does and give the dog to them.
2.  Install an electronic containment system  (invisible type fence)  
3.  Socialize your dog to small animals and teach acceptable behavior while extinguishing bad
4.  Communicate with your neighbors to let them know what you are doing to address their concerns

If the trouble only occurs when the dogs get out of the yard then the containment system will solve most of your problem.  However I would still do the socialization.

Please feel free to call. Dr. Hogan 509-991-0385 until 10 pm pacific time.