TSG, roles, and homeschool

Today I sat at the dining room table for almost 2 hours and called to my 11 and 9 year old that I was available for school work and discussing their subjects. If they come and do school with me then they do not have to correct anything because they do the school with me and they correct as they go. Both ignored me. We have a terrible role issue in the house. Lately, The 9 and 11 year old tell me what they will and will not do with their school and when. They also, lately, refuse to do school when I say I am available and will ask to do school at 5 o’clock with me or 8 o’clock with their dad or I. Their dad cannot do all the school math for 4 kids and chemistry starting at 9 o’clock each night, he has his own work to do. I am here and I am available and they are refusing to work with me. I have thought about a co-op for math or a live online class so that they can fail or pass on their own devices and decide how long they want to stay in a certain grade. I keep telling them that I am the parent and they are the youth and they do not get to make the decisions of what classes and schoolwork they get to do. They only get to decide whether or not to do it and whether or not to do it with me. How do I get my role back as parent/ teacher and how do I motivate them to do schoolwork with me? I am available from 9-2 every day for school. I am frustrated and tired. I just ask for reading, writing, and math every day and am tired of the back talking, rudeness, and them talking to me like I am their peer or their child.