Sorry about your mother. It's a tough time for everyone.
This seems on the surface to be doing her a big favour and appears to be helping your sister and 'what Mum would want'.
After your mother passes away, the childhood demons will re-surface.
Sibling rivalry will emerge big and emboldened when the parent figure departs.
Your sister will still have no asset if she has to go into a nursing home later on.
She will be putting money into something for years and then have diddly squat when she's 88 and needs permanent care or live in carers.
Try to make your sister independent, do not enable her to become the baby/underdog of the family who everyone needs to rescue.
That helps nobody and actually disempowers her to be 'beholden' to you.
Sounds like she needs a sense of independence and control over her own future and finances.
How can you and other family members use this opportunity to really help her with that?
I'd try and find a way to sell her the house at it's current value, eg. a very long family loan with say 1% or .5% interest.
Say 5k a year or something, or even less to start off with or the loan goes up over time as she gets work etc.
She could leave the house to you after her death.
Your sister might be pretty annoyed in 10 yrs time after she has ploughed money into the place but will never own it.
Then if you unfortunately die in 5yrs time, what sort of mess is left for your own family (spouse and/or kids?)
Some older teens might be pretty miffed that Mum says they can't get a new pair of Uggs, but Auntie Joan is living rent free around the corner in Dad's house and she just bought a new car.
I'm thinking of the family relationships as well.
These sort of things can create permanent traumatic rifts in families that continue for generations down the line.