Basically, it is not a problem if input CM is different than output CM.
Actually my problem is that then input and output must have the same common mode voltage, if I i am using VCM = 1.65 V for the output then the inputs signals must have common mode voltage of 1.65 V. This circuit I want to use it to read differential voltage from the bridge circuit, in which basically I can adjust the common voltage of it by adjusting the resistor ratios, but still I dont know if such solution is accepted in a practical perspective. Specially if we take in to the account that next ADC may require different VCM, then how I will be able to change it
The problem with DDA is the DDA itself.
In simple diff-pair, negative feedback keeping inputs equal, while in DDA this statement is no longer true. So, after reaching ≈40mV of input difference, gain is dropped by 10% and for more than 100mV DDA is completely desensitized. In other words, the behavior is like for open loop diff-pair.
Simply, make dc sweep of input voltage amplitude and look for transfer curve (vout vs vin). You will find 3 regions: linear with gain defined by feedback around 0 and two cases with very small gain outside.