His language and threats are abusive. 'Under no circumstances'? 'LET you go'?
If a guy said such things to me I wouldn't simply go ahead and go, however. If you leave him with the kids, who's to say he'll properly look after them, or won't take his frustration out on them? You know him better than we do, of course, but his attitude doesn't sound nice at all.
Really, if this was so important to him, he should already be sorting a babysitter or other childcare, at his own expense if need be, to get what he wants. Hopefully they'd be able to take DS to the competition too, or he could at least do that if nothing else... though I think he wouldn't, if only out of complete spite. How come childcare hasn't come up as the immediate option to compromise with? Or is it that he wants you at home 'in your place' as it were?
Taking care of kids should be a collaborative thing between both parents, he should suck it up that you both have a clash now and work around it with you. Failing that, he takes the kids and watches the game around them, tough luck.
I do think, even if you resolve this well enough and go to the show, you should consider his feelings, or lack thereof, towards you and your children.