NP-hardness reductions
If your problem is with the 100 vertices limitation, then you're in the clear. 
Consider the following reduction: given input $\left( G,t \right)$, if $G$ has under 100 vertices, exhaustively test all witnesses and check if $\left( G,t \right)\in A_1$, this can be done since $A_1\in NP$. Depending on whether or not $\left( G,t \right)\in A_1$ output some constant word in/not in $A_2$.

If G has more than 100 vertices, then your reduction outputs $\left(G,y\left(G,t\right)\right)$. Since you proved $\left( G,t \right)\in A_1 \iff \left(G,y\left(G,t\right)\right)\in A_2$ it's a reduction from $A_1$ to $A_2$. You will probably want (if you're dealing with polynomial time reductions) to show that $y\left(G,t\right)$ is computable in polynomial time.

The asymptotic behavior of the reduction's running time does not depend on how you treat small inputs (in this case, graphs with less than 100 vertices).

Edit: I should note that inputs can get arbitrarily large while keeping the graph small, by increasing $t$. However i assume that (as is with many natural graph problems e.g. clique, independent set) that if $t\ge f(|V_G|)$ for some increasing function $f$, you can simply decide whether or not $(G,t)\in A_1$.