Frustration for sure, E. C.!
Kids not doing what they're capable of, taking 'the easy way out' is usually a sign of anger. She needs something from you that hasn't been addressed and doesn't know how to tell you.
You've had a great deal to deal with during the last 3 years. While you're doing the very best for your children and are an educated parent, something has fallen through the cracks.
Children's needs during their early years are difficult to address often. And while single mothers must take care of life's necessities and their, YOUR, own needs the needs of your children may get tricky.
She's picked an area of battle that you cannot control -- school. Intelligent children do that. Other areas you have no control in are eating, sleeping and toileting. She needs to impose her power and demonstrate her 'unhappiness.' She may not know this is what she's doing, of course. It's new knowledge that has come to psychologists, child development professionals, human development professionals during the last decade.
What is difficult to understand in this may be that TV isn't a big deal for you. She's chosen TV for some reason, probably because it bothers you. Children are very intelligent; your daughter is emotionally intelligent to be sure. TV has nothing to do with school and nothing to do with the 'real problem.'
Getting to the real problem -- her feelings that are driving the behavior -- will take effort, time and probable emotional distress. It's hard to talk about painful feelings, but unless you do the feelings will not change. Genuine, behavioral changes must come from within; she must feel differently to change her behavior. You cannot impose emotional change with punishment or denial. That will only change external behavior.
All people need to have a sense of power about something important in their lives. Children don't usually have many options.
Be careful that you don't misinterpret the word 'power.' In this sense it is not about harm. Power is feeling important. Power is having a voice. Power is making a difference. Power is important.
Your daughter may still feel damaged (emotionally) and very sad about the divorce. She may have lead you to believe that isn't the case. She needs you so won't knowingly say or do something to cause you to leave her as her father did.
Regardless of what has been said by both you and your husband she believes her father left her. When someone important leaves you, you must be a problem (a silent conclusion in her little mind and spirit). She's probably mad and sad about that.
If she doesn't have an emotional language, she may be unable to express these thoughts and how she feels. There are good parenting books about divorce. There are also good parenting books about teaching an emotional language. Having an emotional language will serve her for the rest of her life and her children's lives (should she choose to become a parent).
Talking feelings. Talking about feeling angry, sad, scared, joyful, Talking experiences. Talking about how such and such an experience felt (from the inside).
You're a good mom; you've asked for help. Let her know that you're in this together and that you're not going away. Let her know that she's a powerful little girl doing what she's doing to get your attention. Let her know that you're going to pay attention and support her now. Let her know that something is going on that you don't understand.
Young children think we as parents know everything and must be told by us that we don't! They must hear us tell them that we have something to figure out and sometimes that is hard work.
Let her know that you love her; you can't say or show that enough.
Remind yourself that you're a good mom doing the best that you can! My best to you in this new relationship (the most amazing man!) and, of course, to you and 'daughter.'