DH doesn’t want to care for his elderly relatives

He doesn't have to. Why do you think he does?

Everything has already been said. The only thing I would add is once you start doing something (driving up for every call) you need to keep doing it, so don’t start anything you can’t/dont want to sustain. There are no one-offs in this game.

I'm confused as to why he wouldn't be concerned about his Dad. Or Aunty. If he doesn't want to physically care for them, he needs to sort out people who will. Decline is inevitable and if proper care isn't in place, it'll be crisis after crisis he'll be dealing with. Head in the sand approach doesn't help anyone.

The fact the neighbours keep calling him is an issue that should be addressed with them.
The aunt and uncle are not begging for your son to be their full time carer. It's down to them while they have capacity to either fund their own care, or if there's no cash then SS will step in.
Your husband doesn't have to do any more than he's already doing. If necessary block the neighbours. His own family can speak to him when they need to.
I wouldn't want to be a carer to my elderly aunt or uncle by default. I've got my own Mum and family to think about.

Your DH needs to talk to his Dad and Aunt and arrange a meeting to discuss the future. Do they want to stay in their homes? Will they move nearer him? Do they need carers to visit? Do they think a panic button would help?

Yes he can choose not to bother but, well, that’s just not very nice is it?

Its ok for him to br unavailable. He is not responsible for this kind of work.

There are supported living services that his relatives can pay for if they have money or which willbe funded like other kinds of care services if they don't have the funds, which provide this kind of checking-in. You can also alert social services to tell them these are vulnerable elderly people without family support who should be on their radar in case of issues becoming too much for them.

Agree with what has been said - You need to get some form of local support in place . If they can self fund maybe a vist daily from someone who can help with small tasks, sort meds, even just to have a chat and a cuppa whilst checking they are ok ! maybe a cleaner to do the heavy stuff. Otherwise/ and at the same time they need to be assessed . If you can make appointments and then be there to get the wheels in motion then it will help in the long run . Also have you POA in place ?as this maybe something that needs to be discussed. It is worth the hassle to do this now rather than wait until it gets worse !

They need care assessments, call alarm system to nominated responders, falls assessments, who is calling the neighbours?

I'd talk about everyone having a proper planning session. DH, you, both of them, sister by Zoom. Planning for the future, housing, SS involvement, care, fall prevention and so on. Setting out expectations.

And don't blame the sister, that's just churlish. It's not like your DH wants to do the care either.

“both have had falls/health issues/periods of confusion. When this happens, neighbours call DH constantly telling him they’re unwell and asking him to go and check on them.”

Falls = ambulance really.

Unwell = GP or social services.

Your DH can make these phone calls from where he is, the ambulance operators will forward the message on. Do they have keysafes? If you get these fitted you can register the number with the ambulances and the crew will be able to let themselves in.

I would let him decide. I wouldn’t do it either.

His relatives, his call.

GP first port of call to have them both assessed (I know this isn't easy with elderly people in denial), then a social worker can look at arranging any care needed. They will probably qualify for a couple of welfare checks per day. Or assisted living, if they are prepared to move closer to you. There are a lot of 'ifs' - old people generally want to stay where they are, but you live much too far away to do daily calls.

You support your husband and prioritise your disabled child. Your DHs dad and aunt will have to find local sources of help be that bought in or what the LA will provide. Anything else will lead to burn out.

What do his Dad and Auntie think?

I'm assuming they both still have some level of capacity, so the starting point should really be a conversation with them about their plans as they age and need more support. I do also appreciate that they may be in denial about reality - but an open discussion about what support your DH can provide could be helpful and maybe prompt them to make changes or plans for the future.