got here too late for your first fix.
Just to word it all one more time, with a different view, see:
https://terrylove.com/forums/showthread.php?t=15269
Summary:
Your first "fix" diagram was a good try; nobody told you to raise the elbow to put it right close to the sink. (This gives you more storage space under the sink too.)
So, yes, under the sink, you CAN have a tight radius elbow sending the drain over to the wall, or better said, over to a position in space right above the P trap. Next step: right above the P trap, another tight elbow turns the drain down to the P trap (caveats, re: how far that distance is).
The P trap has to be at the same height as its tailpiece coming out of it (which goes over to the stack). Caveats: 1. Trap weir is the key factor to manage, and 2. The drop from trap weir to the stack is the real thing, which determines the height where you put the trap weir, and 3. tailpiece has to be at least a certain few inches length, number of inches depending on its ID and 4. other caveats etc etc.
When I first posted about all this, I was confused as until then nobody had ever said specifically that one could turn a drain line with a tight elbow...
Hope this helps.
David