Well, I don't know all the details but it sounds like she should have been assessed by an occupational therapist, physiotherapist and seen by the Medical Social Worker when the results of those assessments were known, or at least that is how it is done where I work (OT in Care of the Older Person ward). Unless she self-discharged before they were able to do this of course, or refused to be seen.
Savings - in our area SW England it is £23,250 - over that, she would be expected to pay some/all towards the costs. She would be assessed by the Social Workers to work out what contribution she would need to pay. If she owns the home outright in her name only and no other person (ie husband) living there then she would be expected to sell that to pay towards the costs, but this doesn't need to happen before a care home is found - she could move into one and then sell her house with Social Services paying until she sells and pays them back. I think it is called the 12 week disregard although whether a house would be sold in 12 weeks is another matter! For remaining in her own home and getting carers in to help, again if she has over the £23,250 she would need to pay a contribution up to all dependent on savings, but the cost of the house wouldn't be relevant then. (I think, I am not a SW myself so please check!)
Does she and her carer(s) have suitable moving and handling equipment? If she was unable to stand independently when discharged then it may be she needs equipment, although that would depend on how she moves - some people just need one other person to give them a little bit of assistance to stand or mobilise in which case she probably wouldn't need much - maybe just a zimmer etc. If she needs more help then occasionally equipment up to an electric hospital bed and slide sheets may be needed - it really does depend on her needs and what the carers need to safely handle her. Both a physio and an OT will be able to assess the best for her. I am concerned about you saying carrying her - NO ONE should ever carry another person, they either move them with minimal assistance (eg hand on her hip/back to help her stand or steady her) or they use equipment (hoist etc) or they leave her in bed.
Some people can stay in their own homes even if they are confined to bed if that's what they want. The equipment can be put in, and carers as well, although there is a limit to SS care provision and usually nights are a problem, especially if someone cannot move alone and is incontinent - this poses huge risks for their skin and it can easily break down. Nevertheless it can be done if that is what the person wants. If they can afford it, some people have 24 hour live in carers.
I think, given how it seems like she was discharged before this was all assessed (for whatever reason) and assuming you are in the UK, I would try and get a family meeting/case conference with the professionals. You want a social worker and occupational therapist as a minimum, and a nurse who looked after her in hospital would be helpful. You would all (inc her) talk about her difficulties, how she sees herself overcoming them and what the risks of her remaining at home would be. If she is cognitively impaired in some way and there is a question over whether she would understand the risks then the SW might do a capacity assessment, but if you were all in agreement with her then you would be able to get a plan for her. You want to know a) what are her care needs, esp at night b)can these needs be met at home and then c)what type of placement (carehome) would they recommend if not.
Very sad to hear she is struggling so much and I hope you are able to resolve this asap.