I have an 11 year old dog. She is partially sighted and as a pup was mis-treated by my ex (once - he hit her, I packed all my stuff and left with my beloved pooch within the hour). She is now nervy. I have spent ten years training her, but now that her sight is going she is jumpy. She has snapped in the past, when severely provoked.
I also have an eleven month old daughter.
Because I know my dog can't see things coming up at speed, and because I know she has snapped in the past I have put a LOT of thought, work and money into keeping my child AND my pooch safe from each other. Because BOTH are my responsibility.
My child has never been left alone with my dog. That's just asking for trouble. Likewise my dog eats in the kitchen ON HER OWN. She's an old lady, she doesn't want bothering whilst she eats - I have spent a lot of time teaching her that her bowl and food are mine to pick up and put down, and she will happily let me. But I still wouldn't dream of allowing my child to be anywhere near my pooch whilst she is eating. Because my child simply isn't of an age where she can understand that the dog's dinner is precisely that.... Which it is apparent your child doesn't understand either.
My child has a very large playpen - if I am not in the room with 100% attention on my child and she is awake then I put her in there. Not just to keep her away from the dog, but also to keep her safe from the myriad of other risks any home presents to an unsupervised small person. It's a sad fact that the majority of child accidents and death occur in the home. If you aren't watching them closely enough to stop the dog snapping - then what else could they get into? How often do we hear "I only turned my back for a second!" Dogs, cables, doors.... The truth is a two year old (or younger) isn't capable of understanding the concept of danger, nor of retaining "no" for more than a couple of minutes - so they should never be out of your sight around a dog or any other risk - including learning to toddle with a dog in the room.
My daughter is learning to walk - and when she is careering her V-Tech walker around the room or bombing around crawling I put the dog the other side of the gate. Absolutely NO possiblity for tail treading, running over, crashing into....
And we have a crate for the dog - that is her space, and when she is in there she is completely left alone.
On top of which I am consistently training my dog, around my child, around her toys, around the highchair - the dog can lie under it and won't pick up thrown food until she is told she can, she won't take food from a child even if it's held out.... Because I have trained her not to - and she is older than your dog.
It IS possible to remove the risks by actively considering what those risks might be, and putting in place solutions BEFORE they happen. You didn't do that. YOU left your dog outside (which is something I don't agree with if you don't also provide an appropriate shelter) and your neighbour felt they HAD to move YOUR dog because you had left it out - that's not responsible dog ownership. You LET your child step on your dog - you knew your dog had snapped before, you knew your child was unsteady - as a responsible dog owner you should have anticipated this COULD happen and prevented it before it did. You LET your child be in a position to take food from the dog's bowl, which you could (should?) have prevented.
In short - everything that has happened COULD have been prevented had YOU done things differently. And you want to kill your dog?
I get that you want to protect your children from your dog - but you also have a responsibility to protect your dog from your children. And you haven't. Dog's are lovely, but a truly responsible owner wouldn't have put the dog in any of these situations....