Second ionization energy of group 1 elements is higher than group 2 elements.
When an electron is removed from the alkali metals, they form monovalent cations which have very stable configurations( same as that of noble gases). Therefore, it becomes very difficult to remove the second electron from the stable Noble gas configuration. Hence their second ionisation enthalpy values are very high.
On the other hand, in alkaline earth metals, the second electron is to be removed from a monovalent cation which still has one electron in the outermost shell. Thus, the second electron can be removed easily as compared to alkali metals.