Hi Javi,
I would recommend you to use a tri-state buffer between the SDO pin of the device and the SDO line. It's diagram is similar to the one shown below.
You may invert the SYNC line and let it be your control signal. This way, the SDO line will not be pulled down by the AD5752 and will let you read the EEPROM data without a problem.
In the meantime, I would verify the design of the part from our designers and will get back to you as soon as possible.
Please let me know if you have any other questions.
Regards,
Mark