Is your Husband more strict than you? If so, maybe that is why.
Also, the book "Your 2 Year Old" or "Your 3 Year Old" which you can get from www.amazon.com is real great, explaining the characteristics of each age set. Although written years ago, it is still very enlightening and pertinent.
ALSO, the book "How To Talk So Kids Will Listen & Listen So Kids Will Talk" is great for adults to learn how to talk to kids... and in return, so that our children will talk to us- which is what you want.
I REALLY recommend both these books.
Ultimately, you and your Husband have to be a united front. Do NOT let her play parents against each other. If your girls shuns your Husband... tell her something like "We are FAMILY... your Daddy loves you etc., and we treat each other nicely..."
Or ask her WHY she ignores your Husband. She may not even know why herself, at this age... or maybe she does have a reason.
My kids, sometimes did that to my Husband too. And, we taught them that for Daddy, it was important that when he comes home that they "welcome" him and at least give him a hug. My Husband would actually feel "hurt" if they ignored him. We sat the kids down and explained this.... that it is just our "tradition."
Also, you NEED at even this age, to have SIMPLE things/chores that your daughter can do.... maybe even 3 times a week. Just "helping" the family kind of thing. So that they learn how to be a PART of the family.
For example: when my daughter wants cereal, we tell her to get her own bowl, which we place in a reachable spot for her in the kitchen. BUT, prior to that, she would tell us "I don't know how to make cereal by myself, I don't know where the spoon is..." And she was genuinely puzzled. So, we TAUGHT her and SHOWED her where the utensils are in the kitchen. We at least expected her to get her own bowl and spoon. So we taught her how.
Even my son, at that age of 2 years old, we taught him HOW to "help" and put away things, get a cup of water for himself etc. And he does it. You NEED to teach them that. At this age, they can do simple things... which is in line with their age and development. Both my kids are SUPER independent too.... but we taught them HOW to "ask" for help.... and manners and cooperating as a family, "together." It takes practice... so don't expect improvement over night though. So you have to be consistent.
If my kids balked at even getting their own cup of water for example, I didn't jump up and get it for them. I let them grumble and stew about it and just said "You can do it... you know how... Mommy is sitting down now reading the paper..." and eventually they would get it themselves. Because they knew I would not do it for them. It is "teaching" them that Mommy is not "the maid." And that sure although I do do a lot for them, THEY are responsible too... and in how they ask politely too, and that for me the key being that "they try their best" first. It doesn't have to be "prefect" but that they at least try to "help" and respect that we ALL (Mommy and Daddy included) "help" in the house.
Just some ideas.
All the best,
Susan