I'm afraid of caregiver burnout. What should I do?

I'm the youngest of the family and my siblings all live out of town. I'm a single mom, own a business and am homeschooling my child. My dad moved into a nursing home this spring and my mother had a mini-stroke not long after due to stress and separation anxiety (from my dad). They have a wonderful marriage. Anyway, I'm now living temporarily with her and my daughter because she's lonely and afraid of staying alone at night. People are telling me I'll get burnt out if I don't look after myself because I also go visit my dad every day at the nursing home. In essence, I have 2 parents who need me. I often feel exhausted but I feel as though I can't leave my mom all alone. She's willing to stay in her house until she can. How can I go about this? I was thinking I could get my mom a small dog for companionship (when I can't be there). Should I move back to my place gradually? I don't know what to do anymore.