Your husband should say something since it seems like there's a weird dynamic going on here. If she realizes that he doesn't tolerate that behavior then I'd think she'd stop.

If she sticks her tongue out she goes alone to her room and gets no attention from either one of you.

My 4 year old favors whichever parent spent more time with him in the preceding 24 hours. It goes back and forth. We don't tolerate the rudeness though.

Google Oedipal/Electra complex.

Reprimand her because this behavior is not ok in any circumstance.

Dad needs to remind her that is rude.

And also, does she view it as you are competition with her for attention from Dad? is that a dynamic that is set up? (not sure how, but think about it.. perhaps you say "hey, husband, let's go sit on the porch with this wine I opened and he says no, can't playing with DD"? Then you two are competing for his attention - and she might feel that if she gets it she wins?

So discuss that with your husband, wonder together about what dynamic might be set up or if she is just a really competitive child and is pitting herself against you... some kids are just more competitive than others.

Reprimand her because that is rude behavior.

Does anyone's DD(6) become "mean" towards you if DH gives them a lot of attention? It is so weird, if my DH gives my DD lots of attention, she will suddenly start sticking her tongue at me. What am I supposed to do here with this type of behavior? I want her to have attention from both mom and dad.