Rolfsen's Knots and Links page 10 Exercise 6 states: Let $A$ and $B$ be arcs in $\mathbb{R}^2$ with common endpoints and disjoint interiors. Show that there is an ambient isotopy of $\mathbb{R}^2$, fixed on the endpoints, taking $A$ to $B$. Moreover, the isotopy may be taken to be fixed on any neighbourhood of the closure of the region bounded by $A\cup B$. What if the interiors of $A$ and $B$ intersect?
My problem is that I have no idea how to construct such an ambient isotopy. We can call the two arcs $\gamma$ and $\eta$. I know that the arcs are homotopic by homotopy $F_t(s) = t\gamma (s) + (1-t)\eta (s)$, but extending this homotopy to an ambient isotopy is...unclear at best for me.
I think the idea Rolfson is trying to convey is that I can kinda drag one arc smoothly along the interior of the union of the two arcs, but that would then violate the second part of his statement saying that we can construct an ambient isotopy which even fixes any neighbourhood of the interior of the union of the two arcs.
Is there a better place where I should be looking to get an idea about ambient isotopies and such? It seems like Rolfson is assuming knowledge about these things, but I encountered them in neither Hatcher nor Munkres (for Alg. Top. and Gen. Top., respectively).