You'd want to put the looper dead last in the amp fx loop.

In my rig, I have my looper output going straight into the PA which totally resolves those issues.

Choose a place to put it, anything that happens before the looper will be looped. Anything that happens after the looper will not.
BUT, anything after the looper will change what you hear when the loop plays.


Examples
guitar/looper/distortion = you will be recording the clean sound. You can play it back with or without the distortion. The downside is that the 2nd guitar part will also be distorted or clean.
guitar/distortion/looper = you record the distorted sound. You will always hear the distorted sound. But the 2nd guitar can be clean or distorted.

I prefer to use the first example because I use the looper to design sounds. Having a clean loop gives me the opportunity to tweak sounds in real time without having my hands occupied with that little thing called playing.
But, if you are going to actually utilize a loop for a performance, then you should use the 2nd example because the looper needs to be absolutely last.

The exception to it being last, of course, is if you want to add fx to the loop as it plays. Then it would be almost last.

+1 or at the end of your FX chain if you go into a clean amp.