2+2=2

Teaching my duaghter Math isn't hard, its teaching her in my grandmother's presence. She feels as though tutoring for ten minutes is enough. Tutor in elementary is thirty minutes a day. The worst part, my grandmother agreed to thirty minutes. Its very frustrating because Brooke is fully capable of learning lessons in thirty minutes. This could be an awesome routine to start. Tomorrow, I plan to take her into her room without the tv on, and practicing her addition for thirty minutes. My grandmother can stay in the living with her tv and have no reason to disrupt us. If she has advice, she can wait for us to take a break after fifteen minutes and tell me what she thinks.
I am trying to raise Brooke without disrespecting my grandmother's wishes, but damn its hard. Yesterday, she told Brooke to shut up and I asked her not to. I reminded her that she never hears me tell Brooke shut up because it is disrespectful. She replies, "Well, she disrespected me". I reminded her that's why discipline should be in forced. She got even more upset and said putting Brooke in the corner was abusive. I told my grandmother the corner us best to not use spanking tactics. I explained that I rather her go to the corner for five minutes, then explain to me why she went to corner and why its not safe, respectful or has bad consequences. After I try the corner, and if she is still hard headed, spanking her on her butt with my hand is the next step.
No I don't believe I am a perfect parent, but I am learning. I'm sure these tactics wont always work and I will have to consult with counselors for healthier tactics when she is a preteen-teenager. God have mercy on me...