Can molten Strontium and Barium Hydroxides be electrolysed to give the metals?
Expanding on @Oscar Lanzi comment: first, all the hydrogen (and half the oxygen) would be electrolyzed before then alkaline earth metals.  At that point, if kept liquid, then the $\ce{BaO}$ and $\ce{SrO}$ remaining would be split. That would not be easy, as the melting point of $\ce{BaO}$ is 2,196 K and that of $\ce{SrO}$ is 2,804K (though a eutectic mix of the oxides would be a bit lower).

[It's more efficient to dissolve the oxides in a halide salt. The electrolysis of $\ce{CaO}$ in $\ce{CaCl2}$ has been explored here and here.