Am I responsible if she refuses in-home care while we’re gone for the day?

My story is long, as my mom is young (late 60’s) and I’ve been her caregiver already for at least 5 years (as you sometimes fall into this before you realize you’re in it), but she has had physical and mental/emotional issues for many years prior. Mom has lived with us for many years, and she has never wanted to be alone, even when she was completely physically capable, and had friends of her own, she resented being left at home— I have a husband, and children, and a job, but due a lot to her mental/emotional health issues, going out even for basic simple things (going to work, taking kids to lessons or park) would elicit long sighs, eye rolls, etc. Again, long story (I’ve read a lot about co-dependence, narcissistic personalities, and talked with counselors, it’s helped to know that I’m not crazy :). Over the past decade, but increasing exponentially in the last five years, her physical needs have increased. We’ve crossed the line from, “she’s completely fine, just angry about being home” (while I go to say, school with my kids), to “I don’t think she should be home alone for a long day, I’m very worried about a fall, or a need she can’t meet for herself.” The problem is, she refuses any kind of in-home care in the rare instance that I need to be gone. We’ve talked about it several times, and I just called in a visit from a social worker with the local home health that has been working with her (PT & OT), who tried to help her gently talk through this, and get her to accept in-home care, and again she refused (it was another really lovely counselor in a series of therapists and social workers over the last few years who leave my mom’s hospital room or bedroom, press their hands into mine, and tell me how much I need caregiver support, and to remember that I’m not responsible for the choices she makes, and I so appreciate that... but yet, I have to live with them).

My husband and I arrange everything so that one of us is home virtually all the time, other than a quick errand here or there. But it’s become so hard, so insanely stressful. And here’s my pressing question: this coming weekend, my older son is going to scout camp— he is 12, and it’s his first time having this experience. He’s so excited, but he really wants mom and dad to bring him. We need to leave at 5am, for a 4 hour ride, and then back in one day. Mom is being her typical self about this— out one side of her mouth, she’s saying she wants to come (basically insisting that she will), and hates to be left behind (which she never, ever is), and out the other, that it’s too long and too early for her, and just too much. And it is too long and too early, she will never get up for this, even with my assistance. But, she insists she will— until the last minute, when she inevitably won’t. This is a commitment that I can’t change, or back out of at the last minute, and my son deserves to not have me back out. But my mother refuses to have someone come and stay with her. I can’t plan ahead, I can’t have peace about anything involving planning for any event or even basic simple things. But, at this point, in addition to the years of worrying and tears about this mom of mine, who has really given me a run for my money, am I responsible, or neglectful if she insists on staying home alone, and then has a fall? I’ve never thought this way before, but as she keeps refusing people, and life sometimes needs me to physically leave the house, what do I do?