Sorry, DO but your logic escapes me entirely on this one - why on earth would you expect the other parents to pay half the costs of this flat/house? The only answer is that the other girl pays the market rate for rent for that type of property - which may or may not cover half the cost of your investment ex any legal costs etc. The fact that you have chosen to go without holidays for the next five years is entirely irrelevant - nor should you make assumptions about Parent A's wealth/financial circumstances, no matter how much you disike/disapprove of him and his new family. Which you obviously do. Otherwise why comment on his choice to send his other daughters to private school? Do you know for sure what he's going without (gosh, maybe no hols for the next 5 years...) in order to do so or the type of State school that they would otherwise have to attend?
If you wish to purchase a flat for your daughter as an investment - great - but that's what it is and, by paying you rent, the other girl is doing you a favour, not vice versa!
Not sure I regard it as a mistake per se with regards to giving them an easy life - if it were me, there would be strict requirements in place before shelling out that Daughter knew that the responsibility of 'owning' and maintaning her own property - rather than a rented one - was the flipside of having 'free' accommodation.
In hindsight, I reckon it's a positively good thing that only you are purchasing this property, because, while the girls have been good friends up until now, there is no guarantee they would remain so for the rest of their college life and there would be nothing worse than falling out and not being able to move out. And if you think that was an unlikely scenario, the first boyfriend on the scene that they both fancy will sort that one out.
Unless they're gay, of course.