Wow, that has got to be so heartbreaking!
My first question would be - what/how is she doing in school? If she is having problems there, then this could be an indication that there is a problem that needs professional help. Or at least talking with the school about getting help for her.
Of course, the next question would be - does she act the same way with your parents? Again, if so, then professional help might be indicated.
If she is has no problems with the above - then its time to consider how your interactions with her trigger this behavior. However, it is one thing for a 10 year old to be disrespectful and rude - it is quite a different matter for her little brother to be terrified of her.
And, I will add that when you said that anything that goes wrong in her life is your fault. Makes me think that there are a lot of things going wrong for her. That is what needs to be investigated. Could she have something like ADHD, which would explain alot?
The fact that she is seeing a counselor would indicate that the school felt there was a problem. And, it is a good sign, that there has been some improvement. You might want to try buying "Don't Rant and Rave on Wednesday: The childrens anger control book" It is aimed at the kids from 9 years old and up. Tell her that you would like to see if it can help both of you and then read it with her. Of course you probably should preread it first. Its 61 pages and costs about 11 bucks on Amazon (link below). It has a lot of great reviews by parents and professionals.
https://www.amazon.com/Dont-Rant-Rave-Wednesdays-Anger-Control/dp/0933849540/ref=pd_cp_14_1?_encoding=UTF8&psc=1&refRID=MRQ3KJCKHAZS6QHRK37A
And, as hard as this will be, you will need to also start setting limits on what is appropriate or not. Correctly using a timeout is probably the best way. A good book on using timeouts the right way is "SOS Help for Parents," by Lynn Clark.
Also, try and figure out what some of her triggers are and ways to ease into them or avoid them.
Hope this helps.
Sorry to hear of this situation. I agree that this is the kind of thing that pulls at your heartstrings. She is but a child though and doesn't understand that you let your mom and dad take charge of her for HER own best interest. She knows you are her bio mom, right? I would guess it is a bit confusing and has created some emotions for her that this is her circumstance. That her grandparents raise her and her mom doesn't. Does she know her dad at all? I'm sure at this point, she considers your parents her parents as they act in that role.
Speaking of her parents parenting her . . . if a child in my care is rude or nasty to another person, I have a lot to say about it to them. What is the policy for behavior modification for her with your parents? What is the reward/discipline situation for when she misbehaves or acts poorly mistreating another person? Especially family? This is really important that she isn't treated any different than your typical child even though she has had an atypical upbringing. That is how you train kids to be decent human beings and adults.
You say the counseling is helping her be kinder to your mom. So she is rude to multiple people? ugh.
If she is angry deep down that you gave her to your parents to raise, that will some day need to be dealt with. That's a bit of emotional baggage for a girl even when it is done with the very best intentions.
Anyway, this sounds like a complex and difficult situation. I hope that it gets better really soon!!
I'm so sorry that you're going through this. Maybe you could all benefit from a family counselor?
I agree with SpecialMom in wondering if she's angry that you gave up custody of her but you are parenting your son.
DISCIPLINE DISCIPLINE DISCIPLINE!!! Lack of respect needs to be handled immediately. People may think my comment is too harsh but there are times when an old fashioned *** whooping is great. She MUST understand you're her mother, not a friend that can be talked to any kind of way or a stress ball that can take abuse! She must understand the role of adults and that she is to respect them. I have 3 children and I'm highly stern when disrespect is involved. And do not allow the fact that you didn't raise her make you weak, make it clear, if this is an issue, that you did the smartest thing you knew to do, go to your mother! And let her know you want her to know when she should know when she needs to do the same. You must be strong in your position regarding her respecting you and her grandmother, if she isn't showing your mother respect also.
I think this is definitely an "abandonment" issue. I can't imagine how it would feel to be in your daughters position and feel like she never came first in your life. I also got pregnant the month I turned 18. I had no money, no job, and was basically homeless because my mom kicked me out. My boyfriend and I got married, got jobs, went to school, and took care of our daughter. She knows the sacrifices we made for her, but she also knows she is the most important thing in our lives and how much we love her. At 18 you were an adult and you could've taken care of your daughter. She might not have had all of the things should could get from living with her grandparents, but those "things" don't even come close to comparing to the love and comfort she would get from being lived unconditional by her mother. And honestly if you"don't like her" and resent her, she probably knows that. That, along with her abandonment, are probably way she's acting out. Btw you should know this because you also have your son, but kids don't give a **** about who shows up to their birthday parties or recitals. They care about who is there when they are scared and who sits and plays with them and makes them feel important. You should've found a nice couple to adopt your daughter so she would have parents that love her. I hope you're daughter can work through this, but to me it kind of seems like she never had a chance with the way you choose for her to be raised.