Hello again!
Sometimes simpler explanations are better, eh?
I'm not sure if I'm completely right about what follows, so if anyone refutes me, take their word for it.
Stove burners do indeed emit infra-red radiation. I believe this is because there is alot of electrical resistance in the elements, which causes increased agitation in the molecules of the burner (ie. heat). The extra energy of the molecules can be released as IR radiation.
But the red you see is not IR radiation, but visible light radiation. Don't ask me why, but the burner is releasing 2 different radiations in this case.
FWIW, burners transfer alot more heat through conduction (touching) than through IR radiation. But I'm guessing mom already knows that.
Take care!