It's advisable to take the Part 2 and Part 3 together.. IMHO, After Part 2, it's better to take the Part 3 within 2 or 3 WEEKS..
You don't need any explicit preparation for Part 3. I have read some posts which says that "If you have worked on Part 2, and made the notes then Part 3 will be a cake walk"
So I assume that you bought the part-2 voucher from India..
I am not really sure about what your are referring to "part-2 voucher might get expired in another 2".
Once you bought the voucher, You can download the assignment...
Once you have downloaded the assignment, you have 1 year to submit.. Do you mean that it's going to be one year since you first downloaded the assignment ? In that case, there is not doubt that "YOU SHOULD SUBMIT THE ASSIGNMENT ASAP".
Part 2 and Part 3 are validated together. So think about the option of appearing for part-3 in US itself with 4 weeks..
If that's not possible for you, then certainly you can take the Part 3 from India after 2 months..
I don't see any problem with it, but you may not get any results until you complete part 3.
Since you are in US now, I suggest you to contact SUN either phone/email and discuss you options...