Digital potentiometer as INA129 gain
You don't specify how TPL0102's supply pin is connected (a circuit diagram would be helpful here), but given its absolute max voltage of 7V, it's a safe bet it's not to the 11V supply.

Digital potentiometers only act as such as long as the signals on them are between their supply rails. It's entirely possible that the voltage on the INA129's adjustment pins is outside this range, which will result in the digipot clipping the signal.

Your approach here is a little strange: using an instrumentation amplifier to amplify a single-ended signal by grounding one terminal is kind of perverse. A regular operational amplifier would work fine here; for digital gain control you can either feed the signal through a digipot beforehand as a variable attenuator, use a programmable gain amplifier, or use a multiplying DAC with enough bandwidth (the DDS output becomes the 'reference voltage' for the DAC, and the DAC value controls the output amplitude).