Yes I was going to say that your father should have some choice in this too! It’s not as though we are talking about a young, vulnerable person being homeless. Your sister is in her mid-fifties and your dad may not like the idea of her moving in, even though it’s the obvious solution. And he definitely should not give up his council house.
If she does move in with dad though then at least they should talk to the council together especially if he is at the age when he is starting to need more support. Your sister could perhaps become his carer?
I was going to say as the parent of an adult child with autism, that some autistic people do have problems working ft owing to the sensory overload and exhaustion of having to be around people so much, but if your sister has tolerated working on cruise ships then surely she can tolerate getting more cleaning hours or caring one on one? Or does her dyslexia prevent her from working in a caring role if written instructions are involved? But if that is the case with your sister then she would be better off trying to support herself bc she won’t get extra support like benefits if you are helping her,
Also, you have given your sister a refuge for eight months op. Please tell me she has saved up enough for a deposit now that she has been living with you virtually rent free and had so few expenses?
Any person offering a family member a spare room when they are in difficulty should always thrash out some agreement in advance about length of stay and finances etc, and you, being very kind , did not do this op, but now is the time to step in and say to your sister that this always was a temporary measure, that you and your dh and dc need your family home back and you need the study space. Don’t just make it about you, say everyone has had enough now.
If she is autistic she may need to have this spelt out to her very clearly. And I would also put arrangements in place and say that if this does not happen by July then a, b or c will take place. She may need a big push in other words as underneath everything she may be scared. I know that’s not your responsibility but talk to her honestly about why she has found it difficult to set up a stable life for herself and encourage her to seek support if necessary.
This could be her very last chance with her being the age she is, to step up her working hours and get herself established independently. It will be much harder in ten years time. She needs to crack on with that now and that’s another reason she needs to leave your place and return to taking responsibility for herself.