The two-handed rifle running animations are broken with the left hand clipping through the gun when I move sideways and backwards, a problem that Fallout 3 doesn't have.

I have tried everything but nothing works, I deleted the specific animation files, I tried to add Fallout 3 animations and I tried to get new animations expecting this glitch to be fixed but the left hand always clips through the weapon.

You may want to try to search in Nexus for common bug fixes.
They have a giant patch that fixes MANY bugs and glitches.

I played New Vegas a long time ago and can't remember a glitch like this in it or it didn't bothered me, but I was using a community patch that I've found in Nexus.