Children and finances

My ex-partner and I are divorced a number of years. We have two children under 18. If one child wants to live with one parent and the other with the other. Is it possible to get our solicitors to sign up a legally binding agreement that means each of us with be financially accountable for the child with them and will never be able to make a future financial claim on the other for the child with them, whether maintenance, schooling or otherwise?
Would it be legally binding, without going through court, if we both agree to it?
Thank you.

No it wouldn't be legally binding and even if you went through a Court they wouldn't be able to make such an order.

By law nothing can take away the right to claim maintenance via CMS.

Thank you for your response. How would any possible desired legal agreement work once one, then both of the children are over 18, to manage any further education/ university costs and contributions? The idea is to encompass these financial costs “over 18”, into any agreement as well? Thanks

Once over 18 the child could apply to Court in their own right to seek maintenance from either parent. Up to them to weigh up the cost against the likelihood of being successful