There seems to be alot going on.
Was your sister always close to her grandmother, and what was she doing before granny needed care
How long has she been living with her as a full time carer and did she give up a job to do it?
As an aside, most people have 2 or 3 live in carers if needed, and that costs a fortune, which is why councils who fund it are keener to put them in a home at around £1K a week, as they wont pay for live in/overnight, and max you get is 4 visits a day to check up on you)
Does grandmother own her own home? By your sister living there and caring for her, your sister is preventing the home having to be sold and pay for care, or for paying for care directly - I hope that she is claiming carers allowance and your grandmother is getting attendance allowance, as without that her pension contributions are not being paid.
If she isnt working she is relying on only UC and a carers element to live on. Thats quite a sacrifice when it comes to building a career and personal pension / foot on the housing ladder, and shouldnt be dismissed as 'not working and living rent free.
And yes, she is entitled to a life but has had to resort to teenage sneakery to avoid upsetting the grandmother, who likely was brought up at a time where casual sexual relationships were frowned upon and sharing beds not allowed. Thats a toll, not something to be dismissed again. Would you like to have to act as if you were 15 again?
People have often lived in multigenerational households. Granny might like it. She might not, and ultimately its going to be down to her given its her home and her care. But she may balance things up and think its fine.
Your sister might just really want a child. Not everyone is career driven. If she were to do it 'properly' - ie meet someone, date, get engaged, get marrid, buy a home and then think about a family, she might feel that its a timescale she risks missing out on, so she is grabbing the chance for something for HER while she can. Single parenthood has always happened. It may not be the way you think she should.
Is there a concern that the house will be left to her as she has a baby and lives there? Does granny have the capacity to change a will. You realise she may just leave it to her anyway for the care, she may not even have a will, or she could leave everything to the cats home. Thats Granny's decision.