Depends on both data and question -
Data - Do you have data on patients by way of how many days/months after discharge they were readmitted? Or do you have binary data - readmitted within 2 years, not re admitted within 2 years.
If the latter, use logistic regression - if the former, the cox model. My hunch is you have the days information availbale.
Question - Now, Do you care if the patient returned within 1 month as compared to 23 months? If yes, use cox. If no, logistic regression.
Cox will be able to give you the risk associated with rehospitilisation over the 2 years.
The 'survival' package in R will fit cox models but I recommend reading some intuition behind cox beforehand. Frank harell's notes on his website are a good intro. http://biostat.mc.vanderbilt.edu/wiki/Main/FrankHarrell
Cheers