D.B.
Kids this age don't have empathy yet, so you can't get them to feel things they don't yet feel. That's kind of the theory behind not forcing young kids to say they are sorry - because they aren't! And they think "I'm sorry" is the same as "do-over" - that it undoes what they just said/did.
So they have to be taught what they are allowed to say to others, and what they are not. It doesn't mean they can't have the feelings - it means they can't say them to people's faces, but only privately to you or Dad. You can discipline her for being rude - which is different from being angry at her for having the feelings she has.
I think your husband responded with his own hurt, instead of realizing where 3 year olds are at. I'm not sure that putting hurt back on her, or treating her with the same rejection, is a good technique - it's "eye for an eye" and really justifies her behavior.
She also doesn't have enough vocabulary or depth of feeling to explain the difference between "I don't like you, Daddy" and "I'm a little sad because I realize you've been gone all day and, by the way, it's 5:30 PM and I'm tired. And now Mommy is going to talk to you about your day, and that leaves me by myself." Big difference!
A lot of people recommend "Love and Logic" and also "How to talk so kids will listen...." Those might help you and your husband agree on how to handle these things and give you the vocabulary you are lacking.