Why not apply for a reentry permit: https://www.uscis.gov/sites/default/files/USCIS/Resources/B5en.pdf
It seems designed specifically for cases such as yours - that you are a permanent resident who has had a family emergency which requires you to be abroad for more than a year but that you do not intend to abandon your permanent residency in the USA.
The only complexity is that as a commenter notes, you have to be in the USA to file for a reentry permit. If you can, I’d try to return ASAP and to carry as much documentation with you that shows you haven’t abandoned residency (current mortgage or lease, utility bills, tuition payments, paychecks, etc) and then if you plan on leaving again, filing for reentry just to be on the safe side.