I believe this is false.  There are equisingular families that are not étale locally, nor even formally locally, trivial.   Let $(z,w)$ be coordinates in $\mathbb{A}^2$.  Let $t$ be a coordinate on some dense Zariski open subset $V$ of $\mathbb{A}^1$.  Consider the zero scheme $X$ of $zw(w-z)(w-tz)$ in $\mathbb{A}^2\times V$.  I believe that $\Omega_X$ will have a direct sum decomposition as above for $V$ a suitable open subset.  However, I very much doubt there is any étale decomposition of $X$.  If there were, then the fiber of the projection to $Y$ would correspond to the zero locus of $(z,w)$.  However, the formal completion of $X$ along this zero scheme is not a product, not even after making a further étale base change of $V$.