if i summon tsukuomi and choose to use her effect on herself since it is a trigger effect can i than chain magical dimension to her effect to tribute her for a different spellcaster from my hand??

Yes...no reason why you can't...then the chain would resolve with Tsukuyomi being Tributed and a Spellcaster being Special Summoned and then Tsukuyomi would try to resolve, but since its intended target is no longer on the field, it resolves without effect.