Y or How Can I Stop My 9Yr Old from Mimicking Her Brother

Consequences.

When she lies to you, you give her the same consequences you would had her brother NOT been the one to tell her it is ok. Same thing with disrespect.
And the same goes for him... he lies, you give him appropriate consequences. He disrespects you, you give consequences. If you want to include him telling her to lie to you under "disrespect" then go for it.

You can't rationalize with her that she shouldn't listen to her brother. You can only teach her that there ARE consequences to her behavior. If she chooses to lie, she get the associated consequences. If she chooses to be disrespectful, she gets the associated consequences. Eventually, she will figure out that those consequences aren't what she wants to live with... She might even start to ignore her brother's "suggestions" when she realizes that he might be WANTING to get her in trouble so he can watch her suffer. Yes, boys DO do things like THAT. Particularly, if he has some reason to be jealous of your daughter. And I'm guessing since they are half-sibs and he is just now coming to live with you, that he does have reasons to be jealous... at least in his mind.

Your daughter is old enough to understand that if she wants to copy someone's bad behavior, she will also need to be willing to suffer the consequences for that behavior.

If she does do something you know or believe she learned or copied from her brother, do NOT allow her to use the fact that brother did it as an excuse. In fact, I would tell her that she is not allowed to even mention that anyone else did the same thing. She needs to realize that two wrongs don't make a right; that she has to suffer the consequences of her actions all by herself so she'd do better to make her own decisions; and that no one else is responsible for her behavior. She is old enough to know/learn all of this.

So you can't stop her, but you can give her the tools to make better decisions. You need to stress to her that she needs to be her own person and not follow what others do.

It sounds to me to be a fairly normal occurrence, and she will love him even more for teaching her these things. When you catch her lying, you can try to discipline her, such as you ask her to clean her room she says she did, but didn't then give her a time out in her room, until she cleans it. Do the same with him, but if you catch him lying, say you tell him that he can't go to a party, but he goes anyways and you find out, ground him, and stick to the grounding, make it something like "you are grounded, which means that you do things WITH us, nothing alone" lock his window if need be. Eventually at least she will see that lying gets her and him in trouble.

p.s. never discipline them the same way or in the same place in the house. They will find it fun, and get even worse.

Your daughter never lied, that you knew about. Or disrespected you to your face.

If you don't think you can control a 15 year old boy, then you most certainly cannot.

If you think you can, then you most certainly can.

Hold them accountable. Unfortuantely and contrary to what some parents want to believe, we can not FORCE our kids to do ANYTHING. What we do have to responsibility to do is to teach them right from wrong and to discipline them when they do not follow the rules.

I would like to suggest getting with your husband and setting the perimeters for when one of them lies or breaks a rule. I have done this with my husband and in serious areas told him that I really need his support but that even if he doesn't I feel so strongly about this I will do it with or without his help. Since that is not how we normally do things, when I say that he sits up a little straighter and realizes that it is something I find important enough to "break the code"
Once you have the guidelines set sit them down and tell them these are the house rules and these are the consequences when you break them...that it is nonnegotiable. They are old enough to have it explained to them that these rules are to prepare them for a life outside of the household.
Accountability is key! We have to make sure we stick to the plan but also reinforce the great behavior when we notice a change.