Not an easy situation. It starts with your mom. Living with her is like co-parenting, the two of you need to be on the same page. But YOU are mom, ultimately she needs to defer to you, she had her chance to raise her kids.
I have an 11 year old who is also a fan of you tube and other time waisters, I am not a fan. I have a rule that none of these things are allowed unless all other homework and chores are done, and then it is still a limited pre determined time limit.
There is no discussion, no yelling, if she gets snotty "thats one" if it continues "thats two" continues "thats three" and then she either gets a time out with no electronics or something else that will grab her attention.
Your mom needs to understand that you are taking the computer away because your daughter is abusing the right to use it, and because it works. But everytime she starts a fight with you about it she is undermining your authority as THE parent and allowing your daughter to find an easy way of controling the situation so she gets what she wants. Kids are by nature manipulative, it's normal, but we have to show them that it is good behavior that will get them what they want. They still have control, but only of themselves, and if they use self control they get what they want.
Hope I helped, good luck.