A.G.
It sounds to me like she's just testing her limits in her new home. This is very normal and healthy, especially considering how much she's been through. Her reaction to this major life transition and its resulting behavior could have been MUCH worse.
I'd go a little easy on her for the time being.
She's obviously old enough to know that you and your husband aren't really her mom and dad, but I'll bet she kind of wishes you were. She's also old enough to know she has to follow some rules, but needs to find out for herself what the consequences are for misbehavior in her new environment... thus, she's acting out.
Stand strong on your rules, but keep the consequences gentle at first. Also, make sure you reward her when she does something right. Make a downright big deal out of even minor successes for a week or so. Positive reinforcement almost always works better than disciplinary tactics with kids her age.
Only discipline her when she's really done something bad. If it's a minor offense, don't ignore it of course -- just explain to her why her behavior is unacceptable and then give her a SHORT time-out. Once she's finished her time-out, ask her if she remembers why she got the time-out and make her promise she won't do the same thing again.
(Of course, she will, just to see if you're serious. Expect this, and don't let it upset you. Just calmly remind her that she's been down this road before and she ended up in time out. Ask her if she wants to go to time out all over again. If she continues the behavior, it's back to time-out to do the whole thing over again until she realizes that you really do mean business!)
Then, as the second week goes by, slowly ease up on the cheering squad while simultaneously bringing her punishments up to the same level as what your kids are used to.
Always try to remember that this is all new to her. (Even if she did spend time in your home when she was little -- three years is an eternity to kids this age, she likely doesn't even remember her previous stay much.)
Also, and this is VERY IMPORTANT... make sure to have a talk alone with your older daughter about why your cousin seems to "get away with" misbehaviors she would normally be punished for. Let your daughter know that your cousin won't be living on Easy Street forever, but that learning to be part of a whole new family is hard and you all have to be understanding toward your cousin for a while.
Kids are very willing to help others learn... maybe you could even enlist your 7-year-old's help in coaching your cousin to behave correctly. (Don't forget to give your daughter positive reinforcement for her efforts, too!)
Don't worry too much about your two-year-old feeling slighted... at her age, she doesn't even have the cognitive capacity to truly understand or remember "fair -vs- unfair". She's going to throw a fit when she doesn't get her way with or without your little cousin living with you!! ;->
Seriously, though. It sounds like your cousin has finally landed in a safe, loving environment. You, your husband and your children have the opportunity to do something truly special for her that will affect the rest of her life... it won't be easy, but from what you've written, it seems like you're a wonderful family and you'll do just fine. I think you're wonderful for stepping in to help a family member in need. All the best of luck to you!
A LITTLE ABOUT ME -- I'm a mom to a wonderful, very headstrong 13-month-old. I have one bachelor's degree in Early Childhood Development and another in journalism. I write about parenting issues for a living and have worked with so many kids over the past 20 years, I can't even count them all...