The AC is 1 VAC, 400 hz, while the DC is 1V.
If you have a 1 volt DC reference voltage then apply that to one end of your transformer secondary (and use the other as input to your ADC) and forget about the op-amp because it just isn't needed. However, you still need to do the numbers game.
You say your AC voltage is 1 VAC and that, without further context means 1 volt RMS and, if we assume a sinewave, that becomes a peak-to-peak voltage of 2.818 volts so, in order to lift it to a wholly positive voltage, the DC offset would need to be 1.414 volts.
I am trying to lift the AC voltage from 1,-1 to 0-2 with offset of 1
Now that contradicts 1 VAC so, you have to make this decision but, either way you can apply an offset DC voltage to one of the secondary wires and use the other as signal input to your ADC.
Would combining these two compromise the isolation of the AC and DC
You can't make an omelette without breaking eggs - with both connected to each other there is no isolation between them (and neither would there be isolation if using an op-amp summer) so, once again, you have to decide if this is important to you or not much of a big deal.
One further bit of advice - use an RC filter just before your ADC to give a little bit of anti-aliasing and the bonus is that the resistor will also act as a current limiter should the actual AC p-p level develop into a larger signal under recognized fault or overload conditions.