Not sure what you mean with “side-chain” here (this is a term usually used in the context of compressors) - do you mean that you are running the effect in parallel to the output of the rack? Maybe a screen shot of your routing could clarify…
Usually, my effect plugins are embedded in the instrument rack (e.g. EQ after an instrument) or contained in their own rack (because I don’t want to have any plugins at song level). I use plugin racks either as send destinations (I create a route from my instrument to master out, another route to the plugin rack and set that plugin to 100% wet) or I use them as inserts (running the output from the instrument through the plugin rack).
Your issue “makes the instrument rack too loud” sounds like you are running the effect plugin as a send, but you haven’t set the effect to 100% wet, so you’re still getting some of the original signal, which then of course adds to the original. could that be it?