Suppose we have a projective, nonsingular, convex variety $X$, $\beta \in H_2(X,\mathbb{Z})$ and a family $$ \begin{array}{ccc} \mathcal{C}& \to & X \cr \downarrow& & & \cr B & & \end{array}. $$ together with sections $\sigma_1, \ldots, \sigma_n: B \to \mathcal{C}$ making the diagram above a family of stable maps from $n$-pointed genus $g$ curves over $B$, inducing a map $B \to \overline M_{g,n}(X,\beta)$.

Assume $B$ is a smooth curve and all fibres $\mathcal{C}_b$ are smooth except for one fibre over a point $0 \in B$ which is a curve with one node.

**Question:** Is $\mathcal{C}$ being smooth a sufficient criterion for $B \to \overline M_{g,n}(X,\beta)$ being transverse to the boundary? If not, how could I try showing transversality (or computing the multiplicity of the intersection)?

If this helps: I only need the answer for $g=0$ and $X=\mathbb{P}^1 \times \mathbb{P}^1$.