Frequency mixing at low frequencies (with AD835)
I haven't used the AD835, but I would expect it to work right down to DC.  (That's easy to check)  The two multipliers I have used (AD633 inexpensive*) and AD743 are lower frequency.  As you know the output amplitude is very sensitive to the voltage level, so I'm going to guess that your amplitude difference may be do to layout and stray capacitance.  Perhaps the  1 MHz is being attenuated somewhat.  How big a difference do you see?  

*if you can apply the term inexpensive to an analog multiplier.