Your situation is complex. However, I have a suggestion for part of it. Stop taking away things as discipline. Taking away a toy that is unrelated to the wrong behavior doesn't teach her to correct way to behave. It just makes her angry, as you've learned. Make the consequence related to the offense.
My daughter uses a form of time out that works for many offenses related to getting along with parents. For example,when a child back talks, they go to their room until they can come back out and apologize.
When they refuse to do something, they go to their room until they agree to do it. They can then come out to do it.
So, when she's disrespectful, tell her that she's being disrespectful and send her to her room and tell her she can come out when she apologizes. Do this after you've at first spent time with her when all is calm and have explained the plan.
Calmly discuss what actions/words are respectful and what are disrespectful. Include her in the conversation by asking her what she thinks is respectful and what is disrespectful. Make it an open and friendly discussion over several days.
As to the situation with your father, have a calm friendly discussion about what is happening with the numerous toys and gifts with the goal to come up with a plan that is acceptable to both of you. Be willing to compromise. Suggest that both of you will have to compromise. An example of a compromise could be to agree that he can buy her something once/week or that he can spend a set amount of money per month.
I'm a grandma and I had difficulty with buying too much. It is such fun to have a little one who is so pleased with gifts. And......as a grandparent, we are now more settled, may have more money, and want to provide more than we had as kids or were able to give our kids. Also, it really is a grandparent's job to spoil their grandkids to a certain extent. Did you have a close grandparent growing up? Mine thought the world of me and were able to pay more attention to me than my parents much of the time. I thrived under their unconditional love that did include things my parents couldn't buy me. They were much more reserved about it than I was with my grandkids because they lived in another state and didn't have much money.
When you live with your parents I suggest you have more going on than just gifts and spoiling. Your parents are also parenting your child. You need to find a way to agree on how to parent your daughter. Spend time, over time, talking about parenting roles. Together, make rules and decide upon consequences for misbehavior that everyone can agree to be consistent about.
Talking together needs to go on every day as you work out a plan that everyone can agree upon. Only talk when everyone is calm and nothing is going on. Perhaps have a set time each week when the adults get together and talk about the week and decide what worked well and what you want to change.
It is very very important to be calm and consistent in discipline. Always send her to her room when she's disrespectful. Tell her she's being disrespectful and to go to her room. You may have to guide her there at first. When she does come out and apologize, repeat why she was sent to her room, ask her what would be appropriate way for her to act, and give her a hug.
Which reminds me. Focusing on what she does right more than what she does wrong makes a big difference in behavior. Give her lots of legitimate praise. Experts say we should tell a child when they're being good 5 times more often than telling them when they've misbehaved. Watch and catch her being good. Children want to please their parents. Work on making your relationship with your daughter a positive, loving and friendly one. When you have to discipline be sure to remain calm and use a neutral tone of voice.
I found Love and Logic by Foster Cline especially helpful both when I was raising my daughter and now with my grandchildren. I think you can find it in the library or look it up online for a summary.