Your elder daughter’s talents and interests lie in academia.
The younger’s are in music, and she is more average academically.
Whst isn’t in question is what is best for the younger child, but what is best/fairest for her big sister.
There’s a lot of posters making the assumption that private = better than state.
From your reference to kindy, I wonder whether you are not in the UK. If so, is the selective state school that your eldest goes to the equivalent to a UK grammar school (one where a small number of children are creamed off depending on performance in an exam aged 10)?
From an academic perspective, our local grammar is head and shoulders above our local private school. The private school has amazing facilities, and gives really good support for those who are less high-flying academically.
Therefore, if your elder daughter’s strengths and interests are in the academic, she may not be as well served in the private school - she may still be in top sets, but they may not be quite as academic as the environment she is thriving in.
I am not sure what private education offers her, except the knowledge that her parents are as willing to spend money on her as on her sister.
She already has this knowledge as you are offering her to opportunity to change schools and you are facilitating her to gain more knowledge of the school so she can make an informed choice.
You are making it clear that you would be happy to invest the same time and money into any interest she has as you do for her sister…it’s just that her interests don’t require so much money.
I am one of four. The eldest went to a good private school, the rest of us to state school (my sister and I to a grammar). I don’t think there has been a single moment than any of us have envied my big brother for the money spent on his education that wasn’t spent on us, or felt that it signified that my parents loved him more. We all went to the school that was right for us.
The thing that is important is to show that you care equally - you celebrate their successes equally, you console them for their disappointments and support them in their difficulties equally, you demonstrate that you understand them as individuals. This last point may well mean that you spend more money on one than the other.
I would say that you might want to make sure you have a plan for further education/training (for both girls). It may feel bitter if the elder sister has a difficult time accessing higher education for financial reasons, when ‘all the money’ has been spent on her sister at a younger age. However, I don’t agree that the equivalent should be put aside for her just to use as she wishes when she is an adult. That isn’t fair on the younger sister who can’t help that her needs aren’t catered for as well in the state system.
I guess what I am saying boils down to; make decisions that show an equitable support for both children. This may not be the same as equality in expenditure.