That's normal... kids go through phases.
Tell your Husband not to take it personally.... 3 is a hard age and they are becoming more communicative as well as independent. It is a developmental stage.
The book: "Your 3 Year Old" which you can get from Amazon is a great series. It merely explains what a 3 year old is going through. Although written years ago, it is still very informative and pertinent.
A "Dad" is very important in a girl's life... no matter what. But if the Dad is always scolding and punishing... it may in the long run, make the relationship harder. A Dad... should also try and be a soft place to fall for the child/girl. THAT is really important... to build a good relationship, not it being all about "discipline" or scolding. A child/girl, ALSO learns about relationships from the Dad... and her being able to express herself to him, her Dad being an example of what a man is. Not one that a girl has to avoid or think that they are unapproachable. A Dad... has to think down the road... when she becomes a Teen. If a girl knows she can talk with her Dad too... and trust him and that there is respect.... it makes the child more centered. And she won't seek out outside sources for validation or acceptance. Very important. Your Husband had to think about that.
My Dad, always made sure that we could come to him for ANYTHING under the sun. But he "guided" me as a girl, not always judging me or scolding me but "teaching" me what is right/wrong/valued/ what love is etc. Even if I was not "perfect" he ACCEPTED me... for who I was and what I was going through. Not being intimidating. But GUIDING me. I felt valid to him... not just something he was always thinking I was wrong or impertinent.
It is not all about who is the better discipliner or who is the stricter one, or who the child listens to more. Sometimes a child will just do it or not, based on fear. That is not what teaches a child, the best.
Teach your girl about feelings AND how to express it. Teach her the words for how she feels. ie: happy, sad, mad, angry, frustrated etc. And that she CAN tell you both. And that, even if she is grumpy... she can tell you and you are all a TEAM about it... and will help her... and that's what a FAMILY is... that you all help each other... and try to be nice. That you both lover her and it is NOT a "competition" because of her.
I ALWAYS tell me kids, that it is okay to be upset... but that we talk about it. Sometimes when my Husband scolds my daughter for example, and she is upset... I listen to WHY she is upset... and sometimes, my Hubby is wrong. BECAUSE he assumed something about her that was not correct... he didn't give her a chance to explain her actions. And then so I take her hand and we ALL talk about it, I help my daughter to "explain" to my Husband why she has hurt feelings... that he scolded her but she thought he meant something else.
I teach my kids, that THEY have a voice too... and they can express themselves to us, and that together, we will help navigate them.
BECAUSE at this age although we have to teach them about "life"... they at 3 years old are not grown up, and they are NOT perfect, and they are going through lots of misunderstandings too... and if they choose Mommy over Daddy... they are flexing their "ability" to feel... and kids do feel more cozy with Mommy.
But... in their time together.. have your Husband do things that your daughter enjoys... not always him telling her what to do or get lectured or scolded for everything. I think, maybe your Husband feels "discipline" is more important... than nurturing a RELATIONSHIP with a daughter. That is a big difference. And when you are back in the picture, it is not that she doesn't like him... it is just that she probably missed you. But teach her, that Daddy gets hurt feelings too.... and it is not nice to dis him. And teach her that it makes Daddy sad.
Tell your Husband, the more he gets mad at her for this... the more it will hurt their relationship and it should NOT be a competition. HE is the grown-up... not the child.
My Husband went through that too... with our kids. But my kids just feel I understand them better... my daughter actually told me that. So my Husband makes an effort to understand his daughter... as a Man... and then she feels better about him. He even brushes her hair and even paints her fingernails and lets her put make-up on him, and does girly things with her... they spend time just talking about stuff and he lets her tell him about HOW she feels instead of always "correcting" her every thought and feelings. THAT has helped a ton. And so now, she actually feels close to him, too. He has to soften up... I told him she is a girl... she is tender-hearted and NEEDS you too, so let her need you....
They actually have a great relationship... and she goes to him with problems too... which is what you want for a Daughter and Dad. He actually listens to her... to learn about her, too.
Encourage your Husband, to NOT take it personally... but rather, how to see his girl for the little girl she is. Being 'harsh' with her will only dismantle the closeness.
Little girls need and love their Dads too... it is NOT about being tough with her.
If a child always sees that their parents are competing about who is "better" or not, about discipline or not... its not good for any child. Then it becomes about what the parents need... NOT the child.
All the best,