GGA functionals requiring second derivatives?
It turns out that my original reference is now somewhat out of date, and it is quite possible to compute the relevant properties without resorting to second spatial derivatives. [Johnson1993] has a nice overview of the relevant math, including clean derivations of both YLP and B88 functional terms, and states:

Note that Eq. (7) does not require evaluation of the spin density second de- rivatives as is necessary in many other formulations, a major computational advantage [48]. The fact that these can be avoided has been previously noted by Kobayashi et al.

Johnson, B. G., Gill, P. M. W., &amp; Pople, J. A. (1993). The performance of a family of density functional methods. The Journal of Chemical Physics, 98(7), 5612–5626. https://doi.org/10.1063/1.464906
and
Kobayashi, K., Kurita, N., Kumahora, H., &amp; Tago, K. (1991). Bond-Energy calculations of Cu2, Ag2, and CuAg with the generalized gradient approximation. Physical Review A, 43(11), 5810–5813. https://doi.org/10.1103/PhysRevA.43.5810