Having him neutered isn't like turning off a switch - his hormone levels are
changing and he needs time to adjust to those changes. How are you petting
him? - Is it different from how your little girl pets him? Some rabbits
only like to be petted in certain areas - I have one who refuses to let you
touch his ears, but is fine with everything else.
If you're afraid of him -(understandable if you've already been bitten) then
he will sense that and be afraid too. Try putting a pen around his cage and
just sitting in there with his salad next to you and let him come out to get
it. Don't try petting him until he is comfortable enough with you to come
out and eat next to you - maybe even have your little girl sit with you.
Even if you are still considering giving him up, which I hope you don't, his
chances of finding a home are better if he is at least socialized - and
they don't have very good odds of finding a home to begin with.
Steve