my original reaction was get rid of him but tell me, I still would if you have young children, but if your DD is 16 then you could give him another chance. Importantly, you say that your daughter wants to keep him.
There is a but here, possesiveness is a serious issue. The fact that the dog has issues needs to be addressed and fast, you need to be 100% that you can deal with it. Firstly, take his toys away, we had a dog with possesion issues, he was a rescue and came with them, so much so that we had to leave the room when he was eating! But with time, he was an angel. Dogs dont want to let things go because they feel threatened by it. If you make it clear to the dog that you are not wanting to take things from him permanently then he wont be so bad. We used to play swaps with our dog, oh and add food to his bowl while he was eating. He ended up being a lovely dog (no longer with us).
It could be a dominance issue and the fact you have castrated him may help, it does take a few months for all those male hormones to settle. He may well settle.
Try to resist playing tug with him, things like that. Also, if you need to take something from him grab him firmly by the collar first. Our dog was terrifyingly possesive, he would bow his head over what was "his" and snarl. It took time, but we got there.
I have to ask, seeing as he is your dog, have you done any formal training with him, if not you should! Also, has he been teased (in a kind way) by the "i'll get your bone" game. That often contributes to possesivenesss.
I have worked with lots of dogs, the only one that frightened me was a golden retreiver. On the whole they are adorable, but they can be very dominant.