If we have a $G$-Galois branched covering $Y \rightarrow \mathbb{P}^1_R$ of curves over a complete DVR, $R$ (assume $R$ is equi-characteristic $0$, and let $t$ be $R$'s parametrizing element). Assume that this cover branches only at horizontal divisors (meaning it doesn't branch along $t$ - the closed fiber). Is it possible to blow $\mathbb{P}^1_R$ however many times (call the resulting $R$-curve $X'$), such that the map $Y' \rightarrow X'$, where $Y'$ is the normalization of $X'$ in the function field of $Y$, is branched (also) along some irreducible curve of its closed fiber (meaning it branches along some vertical divisor)?

If so, what would be an example?