It doesn't seem like Munchausen by proxy. The mother cried whenever she gave it to her, so she knew it was bad, and with Muchausen, they generally do it because they want to be a caretaker, meaning they want the proxy to be sick. That was definitely not the case here.
She gave it to Arina specifically when she was in pain, my guess is that it was a painkiller used as a palliative drug (meaning it makes you feel better but doesn't extend lifespan at all, morphine is commonly used for this in patients with terminal cancer and such). A drug that will cause addiction/death/whatever in a year is fine in a patient who is going to die from something else in 6 months.