I can't comment on whether your daughter will be able to cover her outgoings etc.
However, I can share my experience re shared ownership.
We purchased a new build 3 bed house on 25% share in 2008, and sold in 2015. This was in the SE, prime commuterville (my DH worked in London at the time and was within walking distance to the station).
At the time we could have afforded a two bed flat outright but we had a young child, wanted another and had a dog- we therefore wanted more than a two bed flat with no garden.
The combined cost of rent and mortgage was about the same price, maybe £100 more than we would have spent renting the same thing - but obviously the plus side was it was ours, the landlord couldn't suddenly decide to sell/we could decorate how we wished etc, no issues re dog.
However, unlike a private property the value did not increase over the period we owned it at the same pace. When we bought it the total value was £315k. When we sold it it was valued at £400k.
You/estate agent don't value it. You have to pay a surveyor (was about £1k) and they set the price. That's it, no negotiating.
As a comparison, a friend bought a 3 bed first floor maisonette at more or less the same time, and sold it within 3 months of when we sold. It was about a 5/10 min drive away. They bought for £195k and sold for £400/415k (can't remember exactly which). It meant we had built very little equity for our next move (25% of the £85k increase). Our salary had increased over time and so we could make a small step up to a bigger 3 bed and a box room home, but we had nowhere near the equity built up that friends had who had bought privately, and hence had a much bigger mortgage on the next home (which was cheaper than others' next step).
One other thing was, our house was one of four on the estate that was SH (there were several flats). However, having spoken to the builders etc, the finish on the SH was way below the private sales (They had to do a lot of snagging issues in the first 12m).
We had no problem selling it, altho we did a lot of the legwork ourselves. Prospective purchasers had to go through the financial checks etc, but we had to do viewings, photographs etc, no one came out from the management co. Which then grieved me when they wanted their %. I felt we had to do more work than in a traditional sale with normal estate agent.
If I were to go back to 2008, knowing what I know now, would I do it again..... probably... we needed a HOME at the time... but was it financially the best move for us, no.
What I would worry for her is the financial consequences for a few years down the line. She will be spending a lot to keep the flat... but without it growing in value at the same pace that will enable her to make the next rung of the ladder. She may find herself stuck in that what she can take out is not enough to then buy conventionally later on. If she had no where else to go, then it might be worth it... but as she has a nice home at low cost with you I would have thought it not the best choice.
Good luck