I would say that ten years past the point where most young adults are moving out for the first time is fairly delayed gratification, personally.
It makes it more A's choice, rather than being told 'You have to move out by Tuesday', it gives her the 'This is permanent', not 'I'll just stay with Auntie for a couple of days and then go back'.
One of the worst things for inflammatory conditions (or hypermobile/EDS ones) is inactivity/relying upon somebody to do all the (literally in some cases) heavy lifting. It doesn't matter how tired A feels, as a grown up, she has to do things for herself and if her current lifestyle is one where Mum does all the washing, shopping, cooking, cleaning, going out, working, paying the bills, everything - well, if she's always refused to do things because she's too tired, too sore, etc, etc, she's never going to do them for herself if there's somebody else who can be persuaded into doing it for them.
But if she's in her own place, through her own choice because she doesn't want to be in the same house as a tiny puppy, she has to learn to do them.
Being kind and gentle doesn't always work with people who are almost determined to be where they are most comfortable. She could have resisted every suggestion, every hint, every bit of encouragement - even now, your referring to loving living with her Mum suggests that she isn't looking to become an adult, responsible for herself and her own life, but wants to remain a child.
Remind yourself - this is an adult woman who still wants to live with her Mum looking after her 24/7. Allowing her to stay in that helpless infant mindset is not doing her any favours mentally, emotionally or physically.
It's time to grow up. It's time to move out and become independent.
And if a tiny, defenceless little puppy is what it takes to make her take those tiny steps to being a grown up instead of an adult wanting to remain a child, well, it's a hell of a lot kinder to make it her choice rather than snapping and saying 'Go. Go now. I've had enough'.