Let $M$ and $N$ be smooth manifolds. Consider an isotopy of $M$ inside $N$. This means that we have a level preserving embedding $J\colon M\times [0,1] \to N \times [0,1]$. Put $J(x,t)=(\phi_t(x),t)$. Hence $\phi_t\colon M \to N$ is an embedding for each $t\in [0,1]$.

If $M$ is compact and $N$ has no boundary, then the classical isotopy extension theorem states that there exists a diffeotopy (aka ambient isotopy) $H\colon M \times [0,1] \to M$ (i.e. a 1-parameter family of diffeomorphisms), extending $J$, i.e. such that

a) $\phi_t(x)=H(\phi_0(x),t)$, for $x \in M$ and $t \in [0,1]$, and

b) $H(y,0)=y$, for each $y \in N$.

Question: how unique is such ambient isotopy $H$? Can any two ambient isotopies $H$ and $H'$ extending $J$ always be connected by some form of second order ambient isotopy?

(The main example I am thinking of is that of isotopies of a disjoint union of 1-spheres inside the 3-sphere.)