grandma sick - urgent travel required

hi - i'm traveling to china last minute because my grandma is sick and i just realized my visa is expired. my flight is tonight and i currently have a roundtrip from jfk to beijing.

my question for the sub is: should i just change my beijing to jfk leg to beijing-->another country-->jfk? is it ok if this is an in-airport layover, or do I have to stay an extra day? thank you so much.