Private schools is a different argument, StuckIn. If you are sending your child to private school, you are often buying smaller class sizes and better facilities and equipment. I can see how that would make a difference, and why people think this is a good option if they can afford it.
I also tend to assume that behaviour is better at private schools, and discipline is stronger (which is going to make teaching and learning easier). However this could be an erroneous assumption, as it is based on The Chalet School, and the odd documentary about Harrow.
But Jilly is right, in my opinion - what makes the biggest difference to children's futures is parental support at home and in school.
I suspect that the OP's dc are going to be fine - they are going to have two parents, both educated to degree level, both, presumeably, convinced of the benefits of education and the need to support their children's learning outside school. That is a hell of a lot more than many children in poverty have.
It sickens me to think that there are children whose parents don't give them a decent breakfast before school, read with them (or even have a book in the house), talk to them, encourage them, feed their minds or support them. Their parents aren't going to care about extra spanish classes or the value of learning a language. Most of these children are going to grow up with no chances at all - and that horrifies me far more than a little girl not getting to do a few weeks of singing songs and learning her numbers in spanish. I wish I knew what the answer was. I am a firm believer in state education - something I learned from my father - a passionate teacher, whose preference was to teach the least able children, because as he said, anyone can teach a child who wants to learn, but there's nothing like the satisfaction of seeing a disengaged, disruptive, struggling pupil's eyes light up when they understand something they previously couldn't.
In an ideal world, state schools would provide far more. Before and after school care for disadvantaged children - homework clubs where they can get support from teachers, as well as some healthy food and some encouragement. Parenting classes, and classes for the parents to help them learn how to support their children's learning. More free clubs - for fun and for learning - languages, arts, sports.
Don't get me wrong - I think the state system does a good job - but it is underfunded and underresourced. Maybe the classes in the OP's dc's school are providing income that is benefitting her children - but the schools shouldn't have to do this to provide the basics - it should be providing extras (the cream, if you like), which isn't what it's doing at the moment.