I don’t know of any package, which already provides all you need, but I think RBFs can in general fulfill your requirements. Regarding the update strategy, this is possible for positive definite RBFs by efficiently updating the Cholesky decomposition of the system matrix, see section 8.4.3 in Approximation Theory and Algorithms for Data Analysis | SpringerLink. I do have this feature on my todo list for my RBF interpolation package KernelInterpolation.jl, but I never found the time to implement it. However, many ingredients are already there and it should not be too difficult to implement the update strategy based on what is already there. And of course any contribution is welcome 
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