From time to time, I think about my mother who is no longer living.
I’m guessing that it’s “welche” here and not “sie” because the sentence is not making a distinction between a mother who’s still living and one that’s not. In other words, it’s functioning descriptively and not to point out or distinguish. Oder?
“Sie” would not work. You need a relative pronoun here, and you have the choice between “welche” and “die”.
With both pronouns it can be interpreted both ways, I guess just like the english sentence, either as an elaboration (“who btw. is dead”) or as a disambiguation (“the one (of my many mothers) who is dead”).
Of course, the disambiguation meaning is not likely - who has more than one mother?
As for “welche” vs. “die” - “welche” sounds more formal.
All in all putting it in a relative clause like that sounds a bit stilted, and I would just say “an meine tote/gestorbene/verstorbene Mutter”.