Leaving toddler alone while napping with baby ??

Ok  so My little 5 month old has NOT been sleeping well lately and it's exhausting 😞. My mom continues to preach at me about how she snuck in a nap when she had 4 young kids and how my dad had a terminally ill mother when he was a toddler and learned to take care of himself. She says my three year old should be able to be by himself while I nap with the baby. Do any of you do this ? I have seen young kids do extraordinary things when needed to in hard times but this is not my situation and I do not feel comfortable leaving him alone to get into God knows what in the house while I nap. Is this abnormal to feel this way? He's only 3 and I stay at home with him. He's not ready for that kind of responsibility in my eyes. Yet I continue to hear it from my mom😡. Does anyone nap and have a well mannered 3 yr old (oxymoron, lol) that sits alone with tv without needing mommy?