IK bugs while aiming

Hello everyone!

Working on my WWII fps and I am encountering TWO weird bugs using the IK system (Unity 2020.3.32f1 LTS)

Adding a video to show both bugs (20s clip) : The video

Bug number 1 : Left hand jittering for no apparent reason when looking around.

Bug number 2 : IK glitching after firing a shot. To do the recoil I am simply changing my right hand IK target, changing the rotation a bit on the X axis to make an up / down movement as well as moving it back a bit to simulate the force. At the end of the animation clip I am setting everything back to what it was before it started. I am NOT touching the left hand whatsoever.

Picture of the hierarchy / how my infantry is organised as well as my animator are here as well : (Well actually Unity keeps telling me that there is an error while parsing so I can't even upload pictures ... nice).

Here is the picture of the hierarchy : https://imgur.com/a/yBLxZj8

Here is the picture of the animator : https://imgur.com/a/F2JlxZg

And finally a pic of my rig : https://imgur.com/a/yNApuJy