Those are some awful experiences!
DH once was chased by 2 GSDs when he was a lad, and he was anxious about dogs until recently really.
I've grown up with them, and begged him for years for us to get one. He eventually relented and we ended up with a Jack Russel-cross who was the cleverest and bolshiest dog I've ever met in my life! He's not with us anymore, after a long bout of ill health, but we had him for 6 fabulous years, and as DH said, you couldn't help but like him. He was brilliant with our DS, who abused him shamelessly!
I don't know whether anyone has mentioned this, but do any of you have RL friends who have good, calm, steady dogs you could interact your children with? Please don't take this the wrong way - I know this could come across more than a little condescending! But can I share an experience with you?
I also have a Dal who is a child-magnet, and is thankfully very well behaved and calm around children. When Dennis, our JR-x was with us, I used to take them both on outings with our Sunday School children, even though there was a girl there who was terrified of dogs, to the point where she panicked at the sight of even my mum's ancient doddery old pooch who could barely shuffle round the garden.
Anyway, I digress. Before I took my boys anywhere near her, I talked her through some basic doggy-body-language, describing how to watch my dog's posture, tail and ears, so she could "read" my boys, and know when they were relaxed. She was 10 at the time, so was old enough to understand what I was describing to her. Also, I asked her permission before I even brought them on the outing.
Once she gave me permission to bring the dogs out of the car, the other kids immediately flocked round them (Ooh, Dalmatian!) and once the novelty had worn off, she would approach in her own time, and could be found sitting within a 3-foot radius of my boys by the end of the day (this was an achievement and a half for her, as she would climb her mum/step-dad/nearest object whenever she clocked a dog even on the other side of the road). That was 3-4 years ago, and by the end of last year, she was comfortable enough to pet them, on her own terms.
Also, she is now comfortable enough to be able to pass dogs on the street, although she does prefer them a little further away from her unless she knows them (understandable)
But basically, what I'm trying to say is, do you know someone whose dog you truly know is placid, and very easy-going, not excitable, who you could slowly introduce your DC to, on an occasional basis?
(again I'm sorry if it sounds patronising, I'm not trying to be, honest!)