To not know how to help?

[Barsketcase]

My cousin is autistic with severe social anxiety, won’t talk to anyone and won’t accept any help offered. My aunt is disabled and is and has serious heart conditions. She is a single parent as her ex passed away when my cousin was a baby.
My cousin, refuses to help out around the house, refuses to work, refuses to even leave the house if they need milk or something on her own due to her anxiety.
She has been offered therapy, support, all sorts of courses to help her get into work and function as an adult but she will not engage and refuses any outside help. She won’t talk to anyone in the family except my Aunt. She will not even be in the same room as us if we visit.
If something was to happen to my Aunt, I have no idea what my cousin would do. I guess she’d end up in supported living or something.
I have offered to take my cousin out for the day but my Aunt said she will not be willing.
Instead, I offered to take my Aunt out for the day to offer some respite but my Aunt doesn’t feel well enough to go out and doesn’t want me to go round as the house is dirty as my cousin isn’t helping. I have offered to go and clean but my Aunt has refused as she’s embarrassed! I don’t know what else I can do!

I don’t think there’s much else you can do!
Just let your aunt know that if she needs you, you are there for her.

There's not much else you can do. Your cousin is autistic and severely affected currently - likely developed mental health issues on top. This is a medical issue, not a motivational issue. If they can't talk to other people or are anxious of the outside world, of course they're not going to "accept help". It's terrifying for them. They may need help forced upon them, in all honestly.

How old is your cousin? I was in their position for a long, long time - but my autism was only diagnosed after it all. I still struggle to cope but doing a lot better in general.

Supported Living would be good for your cousin now. She won't like it at first, but it would have been good for me to get me on my feet sooner. I had the opportunity and was actually quite keen, but turned it down as my mother guilted me into staying with her. She wasn't that supportive.

And on that note, your aunt needs to take some responsibility for her side of things, at least in accepting the help offered. If she won't... Yep, nothing you can do.

She’s recently turned 18. She refuses to leave the house alone and I don’t know how she can be encouraged/forced into supported living to be honest

You need to understand it’s can’t not won’t. I have the misfortune to know a lot about autistic teen girls with severe anxiety. She’s not refusing to do these things, she can’t do them. It sounds like you need outside help. Does she have an EHCP?

She refuses to attend any appointments with doctors, counsellors etc so they can’t do a care plan in absentia

Maybe just phone your aunt for a chat now and then?

I'd focus on getting your aunt to accept your help or she's going to end up in a worse state, and they'll both spiral.

Tell her you love her, you would never judge her, you understand that she can't keep on top of everything and your cousin while she's ill, and you want to help.