Your problem is in $P$. In fact, it can be solved in $O(n^2)$ time.
Given a tree, you can find a label (a binary string) that is a canonical form for the tree (i.e., all isomorphic trees will share the same label). The algorithm also computes a label for each of its subtrees along the way. The algorithm uses $O(n)$ space and $O(n^2)$ time. Compute these labels for $T_1$ and $T_2$ and all of their subtrees. Store the labels of all subtrees of $T_2$ in a hashtable.
There are only $O(n)$ candidates for $T$: since we want $T$ to be isomorphic to some subtree of $T_1$, each subtree of $T_1$ is a candidate for $T$. Given a candidate for $T$, you can test whether it is an acceptable solution in $O(n)$ time: check whether its label matches any of the labels of the subtrees of $T_2$. Out of all the acceptable candidates, keep the smallest one. The total running time to check all candidates is $O(n^2)$ time.
Thus, we obtain an algorithm that solves your problem in $O(n^2)$ time.