Sometimes kids need to let their meltdowns run their course, to get the feelings out. Sometimes they need to work their difficulties out themselves. Inject the situation with humour. I see a lot of orange juice on the floor. Here is a sponge and a bucket of warm water.
Children can use the tools they have, which are dependent on age and maturity.
The problem is that it doesn't disappear, it just goes into a state of suspended animation, and when the TV goes off, the interpersonal dramas that triggered those negative feelings in the first place seem even more intrusive and annoying than they did before. But I know you're responsible enough to work out a way to get your piano assignments done by Tuesday. Don't expect your child to learn behaviours without witnessing them being played out authentically. I spent a winter learning to ice-skate so that my children could see me have humiliating falls without getting angry and giving up. My children's thoughtful behaviours towards me escalated dramatically when I began making an effort to demonstrate similar things publically towards them or my husband.