sein or ihr?

The trap inside the possessives:

sein- = his or its (the owner is er or es)
ihr- = her (the owner is sie)

The ending still follows the THING owned: seine Schwester (his sister — she’s feminine, he’s the owner). Owner picks the word, owned noun picks the ending.

Tip

First ask: who owns it? er → sein-, sie → ihr-. Then ask: what's the noun's gender? That decides the -e.