Galois module structure of the integers in wildly ramified $C_p\times C_p$ extensions

Let $L/K$ be a finite Galois extension of local fields which are finite extensions of $\bQ_p$ and the field of $p$-adic numbers. Let $\Gal (L/K)=G$ and and $\euO_L$ and $\bZ_p$ be the rings of integers in $L$ and $\bQ_p$ and respectively. And let $\euP_L$ denote the maximal ideal of $\euO_L$. We determine and explicitly in terms of specific indecomposable $\bZ_p[G]$-modules and the $\bZ_p[G]$-module structure of $\euO_L$ and $\euP_L$ and for $L$ and a composite of two arithmetically disjoint and ramified cyclic extensions of $K$ and one of which is only weakly ramified in the sense of Erez \cite{erez}.