International travel with inaccurate "middle name" listed on green card and I-797 notice of action for I485 approval

[Neil_Arora]

Background: My wife's green card and I-797 notice of action for I485 approval has a wrong middle name written on them. The full name (including middle name) was accurately listed on all the previously USCIS correspondence (i.e. EAD, I-485 Receipt, etc.). We do plan to prepare and submit the I-90 form to rectify the error, which is taking almost a year to process. 
 

Questions:

1) Given the long processing times for I-90 form, if my wife travels internationally to meet her parents in India, are there any potential concerns / challenges she would face while departing India or re-entering US?

2) Are there any other alternatives (i.e. I-551 stamp) we should consider before traveling internationally?

Really appreciate your guidance in advance!