The really sad state of social care in the UK is such that they really will tell you outright lies and make demands and tell you that you are obliged to do things that you are not, and so on and so forth.
You are NOT obliged to accept her back at home. You can TELL the social workers that you will no longer provide any care for her. You can TELL them that it isn't her home, it's yours, and you will not be accepting her back there. TELL them that it is their responsibility to find her somewhere to discharge her to. Use the phrase UNSAFE DISCHARGE frequently. Don't allow them to guilt trip or draw discussion out of you.
Others are right, FIGHT them tooth and nail. Run everything hospital or social services tells you through a bullshit detector in your brain. Read up on what SS are obliged by law to do for her. Read up around the whole subject, including what they can compel you to do - it's NOTHING.
Sadly it's often a case of last one left holding the baby, has responsibility for the baby. At the moment it is the hospital: DO NOT LET IT BECOME YOU. DO not let it become you "temporarily". You are in a FAR stronger position if you do not allow yourself to be left holding the baby. if hospital transport turns up on your doorstep, don't even let yourself be seen.
You are not obliged to fund, or to provide, her care. The council is. Social Services are obliged to find her somewhere that they deem to be suitable for her. If that is a care home, they must provide funding for at least one, if she has less than 23.5k savings. It may not be a care home of your choosing or within a reasonable distance for you to visit.
I know this sounds extreme. It is. Hopefully you will have a nice understanding contact at the hospital and social worker, but you may get useless ones who want to shove the problem onto you asap.
Do you have power of attorney?
Please join the safeguarding futures and social care group on facebook. The admins are experts and there are a few other experts in there who give their time and expertise for free very generously.