Doris you need to spray up under the leaves, and the stems as well to get the mites. If you do that a couple of times a week for a couple of weeks it absolutely works. Rain doesn't help my brugs either, as it doesn't rinse the undersides of the leaves no matter how heavy it is. Mites love it under the leaves.
I think the idea of covering the pots with plastic instead of trying to move them out of the rain is excellent. Or, do you have a space under an overhang of the house where they could live, so you could control the amount of water they get?
My brugs are all big enough to handle any amount of rain, but that's what I do with my orchids that can't stand our heavy rain here. They live under an overhang on my patio and I either just spray them weekly or might move the whole shelf unit out into the rain once or twice a week to get them watered.