Hi Hamed,
In general for ADNI, a patient is scheduled for different visits at key checkpoints: baseline, 6 months, 12 months, etc .. Since each checkpoint contains data collection of multiple modalities (history taking, cognitive tests, MRI scan, PET scan), they all require different appointments with the relevant doctor or for the scanner time. Not all the appointments can happen on the same day, and they usually can be 2-3 weeks apart. Scans are taken when scanners are available, cognitive tests are taken in batches by different clinical personnel. I'm not sure if history taking and diagnosis are set on a different appointment themselves from cognitive tests (we can find that out in the ADNI protocol/manual).
Regarding those specific dates, I don't have time right now to track down why exactly they are different. The one on DXSUM is likely the date when the diagnosis was set (probably along with history taking). The date you mention in the TADPOLE spreadsheet was taken from ADNIMERGE.csv, which was itself extracted by Mike Donohue's R script from one of the other spreadsheets uploaded on LONI. If you need to, you can check that R script (it's available on LONI, see ADNIMERGE package) to track it down further and read the ADNI manual to find out exactly the protocol. Another solution is to just use one of those dates (or both dates, each for measurements adjacent to them) in your model.
I know this doesn't fully answer your question, but I hope it provides a good starting point.
Raz