just to follow up on this with cheese gate.
I would have allowed them more cheese but said that was all they would get until they ate some of their dinner.
If they then ate the cheese, demanded more, i would repeat what i said earlier, if you want more cheese, eat some of your dinner.
If they started screaming/demanding and refusing to eat i would simply say "I told you my rule, eat more food you can have more cheese.
If they continued to refuse i'd simply tell them i don't respond to screaming, if they don't want their dinner, they can leave it, but i won't be giving them more cheese until they eat more.
Then it is their choice if they eat and get more cheese, and i am not threatening to take their food away. i would ignore any further screaming and not respond to it, other than the odd reminder that screaming gets them nothing, eating gets them more cheese.
Set your boundary, don't shout, be firm, don't budge. repeat the boundary.