Good! Keep at it. You have to be brutal. Be very firm that you can't do any more than you are (even if you feel you can) and that you are struggling with the amount you're doing.
The way rehab works (in England) is that you get up to 6 weeks on the NHS. If at any time during that 6 weeks, it emerges that longer term support is required, she will have an assessment of her needs (make sure you're involved - she'll downplay what she needs because she won't want to admit her incapacities) and a financial assessment. The rehab place won't be withdrawn, it'll be kept going until there's the longer term care in place. But she's liable to make a financial contribution from the date it's decided she has longer term needs - you may not get the full 6 weeks free.
If she comes home with carers in place, the value of her home is excluded from the financial assessment. If she moves into residential care of any sort, then her home will be included in the financial assessment.
As clouds says, if she has capacity, it will be her decision as to what happens, not yours. So you need to be quite brutal with her as well, lay down firmly what you can and can't do. A fall alarm may be suggested - sounds great, but all they do is alert you (there isn't a special team to come round and get older people upright again) so you have to think seriously about how often you can cope with being called out to sort her out. And bear in mind that if it's more than you feel confident to deal with (eg a broken bone, and you can't get her into your car) then the ambulance may take several hours to come, and you'll be lucky to be seen within 4 hours at A&E.
So go into this with your eyes open, and be realistic about what you are able to take on.
That said, even though falls are low priority within NHS, social services take them seriously, and if she starts to have them regularly, things are likely to happen.