Your story reminds me of the older cars I owned back in the 1970's. Tie Rods and Tie Rod joints would wear out, causing lots of slack in the steering and the constant moving the steering wheel left to right and back again just to go straight.
Sounds like your's has worn out parts. You can take the steering wheel off the steering column and reposition it so it's straight again. In the 1970's and 1980's this was a pretty common practice after getting a front end alignment. But, just repositioning the steering wheel does not fix worn joints.
Check the front end steering system, everything. It might be time to do some major repair.