What is right for your mum from her point of view is not necessarily what is right for you and your family.
I am guessing your mother has had a stroke? Sorry to be blunt. She may never recover. There may be damage to her brain that develops slowly. This may be the first in a line of strokes. Or she may recover somewhat. You dont say how old, or otherwise fit she was before becoming ill.
She will be in denial both regards to how much care you have to give, and how her recovery will be.
When my father had his stroke, my mum became his full time carer. Her entire life changed because everything had to be scheduled around him and his needs. She could not go grocery shopping, for example, until he had moved his bowels in the morning, as he needed help with toilet visits. With a body semi paralysed, the internal organs were also affected.
It is a kind thing to do, to become the carer of an elderly parent. (I know, because I am currently struggling with both my parents, as my mum now has alzheimers) But what you have to bear in mind is that your mum has LIVED her life to the grand old age she is now, and you are now in a stage in your life where you are bringing up children, and your life, and your childrens lives are ahead of you, and this will impact on them and everybodys enjoyment of life.
Also, bear in mind, if you bring her home now, it might not be so easy to find a place in a care home as it is now, where the option is either care home or her own home. From the hospitals point of view, care home is more viable than her home, so should be relatively easy for her to get a place. It will be much more heartbreaking for all concerned if she is "kicked" out of her granny annexe in a years time.