I agree, move them outside. If you absolutely must keep the bananas indoors then you need to keep the humidity very high by spraying with water.
There is no insecticide known to man that can cure your spidermite problem, nothing will kill/destroy the eggs. The only solution is prevention or use a natural predator of spidermites
GroWell > Natural Predators (Red Spider Mites) (cue eveil laugh)