Katharine –
Bt-i, the active ingredient in your mosquito control and our Mosquito Bits, will not kill beneficial nematodes. However, using both together may be a bit of overkill — both attack the fungus gnat larvae that are feeding on the root hairs of your plants. I would recommend adding Yellow Sticky Traps to reduce the number of egg laying adults and some sort of mechanical control — Diatomaceous Earth, Gnat Nix — to reduce activity on the soil surface.
As for one product to kill spider mites, thrips, fungus gnats and whiteflies, I recommend MET52. It comes in a liquid concentrate for foliar applications and a granular for for use in soil. The link below will provide more detail on how to get rid of fungus gnats and the products mentioned here.
Good luck!
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