I ask my kid to finish up the dinner because he doesn't want to.
1. You must finish up your dinner .
2. You must finish your dinner.
Is it obligatory to use the “up”?
I'd like to say a bit more on this.
You use "finish up" when someone is almost done. You child may be almost done eating what he or she intends to eat (and it's not a bad thing if some things are left behind, like the starchy, fattening things), and you want him to be done so you can go on to cleaning up the dishes, homework, whatever.
Come on, finish up so we can get the dishes done and you can have your bath.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.