Woah! Be very careful where you go with this! My step daughter (age 13) prefers to be with us instead of her Mom. The reason is that her Mom's husband hands down rules and punishments that are completely inappropriate (and no offense but your husband's suggestion I think is inappropriate and will only make her dislike being with you all the more). My step daughter has absolutely no respect for her Mom's husband and resentment towards her Mom because she feels like her Mom is choosing this loser over her by not sticking up for her. EVER.
Now, I'm not saying that you or your husband are doing any of these things. My point is that this went on for YEARS and my step daughter put up with it because she didn't want to hurt her Mom's feelings by telling her that she hated her step dad so she gave her all kinds of bogus reasons for wanting to be here instead.
One of the very BIG reasons we've discoved that she and her brother (age 11) like being here is because they are allowed to respectfully say how they are feeling and tell us what they want. They don't always get what they are hoping for, but rarely kick up a fuss about it because they feel like they are listened to and loved, regardless of the outcome, and like they can tell us anything without fear of reprisal. The other big reason is that even when they are punished, they are told that they are special and loved, so Dad is never the enemy. He rarely raises his voice to them, never has spanked them, yet they are not spoiled. (And yes, they have PLENTY of chores at our house, so that isn't it, at least not for them.) THE KEY HERE IS COMMUNICATION.
You obviously are hurt that she prefers to be with her Dad and that she was dishonest with you. If you lower the boom on her, you will make the situation much, much worse. I'm not saying that there should be no pusishment for her dishonesty, but you need to get to they heart of WHY she said that and then address it, not only to your satisfaction, but to hers as well. If you don't, this behavior will not only continue, but worsen. That's exactly what I saw happen with my step daughter at her Mom's house. She finally refused to go back to her Mom's in Feb. and has been here ever since - her Mom lost her just because she wouldn't take the time to listen to her and stick up for her when it was appropriate. (My husband warned her for 8 years that this would happen, trying to save the relationship, but she ignored him and lost her daughter.)
If her Dad and you get along well (I think you said you do), then you should talk to him as well and involve him in this. The two of you are her parents and therefore are responsible to care for and raise her no matter who you may be married to. Maybe he already does this, but your hubby needs to give you his input and then step out of it and let you and your child's dad work things out with her. Then he needs to accept and support whatever the two parents decide is appropriate for her.
The bottom line is that she's obviously got an issue that she'd rather lie about than tell you about. Ask yourself why and then fix it, and I'm sure you'll see some big changes in your daughter when she knows you are on her side -all the time, even when she is being naughty.