Mine was like this for a while.
I decided I couldn't live like that. I mean, I seriously could not be on duty 24/7. I was burned out and exhausted and wanted to get in the car and leave. Forever. Seriously.
I left DH with a bottle, a sippy, a pacifier, some pumped milk - and left for four hours. With his full agreement, of course. He HAD to work it out with her. I had told him to call me on my cell phone if it got really bad, if she got hysterical, or if he got overwhelmed. She squalled for two hours and then napped in his arms. I hated that she cried, but it was what we needed to do. We did that a few times, and eventually she learned that Daddy was okay, too - that it was okay for Daddy to be taking care of her. That was critical for me.
She prefers me, because I have the hookup, you know, but she'll spend her entire weekend with him, only coming to me to nurse, and can I just tell you that it made all the difference in the world to me at that point?