The anger that DH is feeling, the stress that will cause him will impact his own health and so have a knock-on effect on your family too OP.
In his shoes, as well as speaking to his Dad and Aunt about their plans for their futures now they're at a stage of needing regular help, I'd also be telling the neighbours what you've said here.
"I'm 1.5 hours drive away. I work full-time and have a disabled child to look after. I can't come. I can't do anything right now, I'm changing a nappy/cooking dinner/at work. No, my wife can't come either, she's busy doing essential things too. If Dad or Aunt are unable to book a GP appointment and take a taxi to the surgery to discuss their problem, then it sounds like an emergency so please can you call an ambulance. I'll give Dad/Aunt a call tomorrow to see how they're doing. Thanks for helping. Bye".
It will flag up to authorities that these people have no help. It will also stop neighbours calling because they know DH won't accept the baton they're trying to pass him. If it's paramedics picking them up off the floor and not taking them to hospital but asking "is there anyone we can call" and they're saying "my son/nephew helps me", DH response above will say loud and clear to everyone that the help he currently provides can't be added to in this way.
Everyone is trying to turn him into their carer and they'll keep doing it because he's not refusing. He needs to refuse in the moment when carer-type things are being asked of him, every time. He also needs to switch off his phone or put it on airplane mode at night. Anyone who is physically and mentally capable of calling him, including his Dad/Aunt, is also capable of calling an ambulance instead. I know the ambulance service is shite at the moment, but he doesn't even live close by so isn't going to be quicker to get them to hospital than an ambulance would. He doesn't need to be available 24/7.
If they get a falls alarm it needs to go to a service that will do more than just call DH. Or it won't solve anything.
One obvious thing. Can Dad and Aunt not live together to help each other out? If they're the types to not want outside help or to move to a care home. It could keep them independent for longer and free up cash from the sale of one house to be spent on help/care services. It could be done legally so they both co-own whichever house they live in and both have 50% of the equity of the one that's sold. Assuming both houses worth similar amount, then neither would be losing out and both could still leave their share to whoever they liked upon death (if there's anything left to leave).
You can't blame your SIL for living her life. She doesn't owe them elderly care just because they provided childcare. I'm sure she didn't ask them for help whilst promising that then reneging on the deal.
It's coming to us all, with retirement age creeping ever upwards, people moving away from their home towns, people having smaller families and working longer hours. Most of us are going to end up in the Dad and Aunt's situation of managing alone at home as best we can for as long as we can, then utilising whatever inadequate measures social services put in place until we end up in a care home/die (whichever happens first). It's not a pleasant thought but it is reality.