Everything seems worse when you're tired. The good news is: you WILL sleep. Eventually. Maybe not tonight, but you will sleep.
Change the things you can. Teach your kid how to adjust the clock, and tell your other kid to stay out of your room until the alarm actually goes off. Then, accept that you're tired. It's not going to kill you. It's uncomfortable, and it makes all your emotions MUCH louder, but it's not a death sentence. Find a way to joke about it, make yourself a nice cup of tea/coffee/go juice of your choosing, cancel any plans you can, and just ride it out.
It's a crappy part of the parenting gig, for sure, and it WILL pass. You can get through this, OP!