Can we donate our qurbani (animal sacrifice) money to go towards feeding Syrian families?
Animal sacrifice on Eidul Azha is meant to revive the spirit of sacrifice in us, following the example of the sacrifice of Ibrahim alaihissalam. It is not primarily meant to use the flesh or hide of animals for charitable purposes. Doing that is a bonus. So comparing animal sacrifice with helping Syrian refugees is like comparing apples with oranges. Animal sacrifice, however, isn’t obligatory. If you do it in the right spirit you reap rich rewards; if you don’t do it you aren’t a sinner, but you deprive yourself of those rewards. A compromise way of going about it could be to do one animal sacrifice of good quality but not very expensive for the entire family and to spend the rest of the amount that you had intended to spend on sacrifice on charity of your choice.
It’s not clear from your above answer what exactly do you mean by “reviving the spirit of sacrifice in us”.
The spirit of sacrifice means the resolve that our life and our death are both available for Allah Almighty, our creator, and we are prepared to do whatever He expects from us in this life. It is revival of this resolve that is desired through animal sacrifice every year. When the knife is cutting the throat of the animal, ideally we should be making that commitment with our sincere emotions.