All the examples I've seen and all the experiments I have tried show that Mathematica scales the two plots so that every x,y in one graph lie on the same x,y in the other.
What if you try the following:
Draw the first plot as usual. g1=Plot.
"Fiddle" with the second plot by changing the second function definition, changing the x and f[x] so that the size and position of the second function will be placed and sized as you want it to appear, ignore the actual ticks. g2=Plot.
Manually create a graphic of line segments and text to simulate that second set of tick marks and labels. g2=Graphics.
Then combine all three graphics with a Show[g1,g2,g3].