Let $E$ be an elliptic curve. I want to consider its degeneration to the union of two projective lines $C:=\mathbb{P}^1 \cup_{x,y} \mathbb{P}^1$ attaching at two points $x,y$. The involution $-1$ on $E$ can "degenerates" to an involution on $C$ that preserve each component $\mathbb{P}^1$ and swaps $x$ and $y$.

My question is, can the translation by a 2-torsion point on $E$ degenerate to an involution on $C$? If this is possible, what kind of action will it be?

More generally is it true that for any translations $t_1, t_2$ on $E$, there exists a degeneration $C$ of $E$, such that all $t_1, t_2, -1$ degenerate to some action on $C$?