Without knowing the age of your parents and their financial position, it is difficult to answer the question. However I am assuming, based on your other posts, that you would be looking to use the funds raised by remortgaging your parents house to buy a house for your sister. If that assumption is wrong, apologies.
Likewise, as another poster mentioned, you can't mortgage something you don't own and if your parents did get the mortgage, the tax position on gifts to your sister would need to be considered. I'm not saying there would be an issue, but it would need to be clarified and if so, dealt with.
As it stands, based on the limited information you've provided, your sister cannot afford a mortgage on her own, simple as that.
To me, the options therefore are limited and the only thing I can think of is for either some/all of your family to apply for a mortgage with your sister and buy a house jointly and let her live in it. If your sister's circumstances changed/improved down the line, she could always considering buying you out.
You would need to take legal advice on this, there have been plenty of posts on here in the past where people have bought property together and subsequently fallen out. The issue of first time buyer status would also need to be considered, if someone hasn't bought property before they would lose it.
One thing that I don't recall you mentioning is the status of your sister's childs father. Is he contributing in any way to support the child and if not, why not and should he? That could improve your sisters financial position