Where to find help with elderly parent who is depressed and becoming unhygienic?

My mother has recently stopped living alone, and my sibling and I are trying to share the responsibility of looking after her. Unfortunately, it is not working too well! We are each noticing that she is depressed, withdrawn and has little idea of hygiene. She has to be coaxed to eat at almost every meal, and much time and energy is spent in talking to her about what we need her to do (eat, change clothes, do a little walk in the house or neighbourhood, do a crossword puzzle etc). She is quite forgetful but seems to not like being told what to do. She often just ignores what we've just asked her to do especially re changing of clothing. She has significant hearing loss. We are getting emotionally drained and desperate. What are the options here? She is the kind of person who would go downhill if moved to a nursing home but we are feeling overwhelmed and can't cope at this stage.