mummy your family didn't even try to figure out why your dog was behaving out of character, they just put it down, that is shockingly unfair on your poor dog. What if it was something that could have been treated.
There is some shocking negativity around dogs here, and no it's not all 'realism' it's just fear. You're right, you can't guarantee that a dog will never do something, but you can make a fairly educated guess that most dogs are safe and most owners are responsible.
I hope you all teach your children how to respond to dogs in public, and no this doesn't mean 'being scared' of them. Teach your children how to recognise dog body language, how to approach a dog safely, how to play safely. It's not always about the dog and if your child can't be trusted around a pet then they need supervising when with that pet, for the pet's safety too.
OP, I am sorry that the country we live in is backwards with regard to dog ownership legislation, breed banning laws are rubbish (German Shepherds are safe in England, but not in Ireland, Pitties are safe in America but not in England) and don't tackle the real issues in any meaningful way, they are lazy 'solutions'.
Saying that, the law is what it is (until it's changed) and it's in your best interests to follow that law, which you have now said you will be. If you're comfortable having your dog sleep in bed with you DD then don't imagine the worst, if you're not comfortable then perhaps a dog bed in her room/next to her bed?