PDA translating $a^{m+n} b^n$ to $x^{2m+2} y^{3n}$
This seems impossible if the translator has to be deterministic.
Let's clean up the problem and ask the PDA to convert $a^{n+m} b^n$ to $x^m y^n$ (your translator can be converted to such a translator by using a regular transducer). Since your PDA is deterministic, it cannot output anything until it knows whether $m = 0$ or not, which can happen in one of two ways: either it reaches the end of input, or it reads $a^n b^n$ (which must also be the end of input).
Now let us modify your PDA so that instead of outputting $x^m y^n$, it checks that the rest of the input has the form $x^m y^n$. We obtain a deterministic PDA accepting the language of all words of the form $a^{n+m} b^n x^m y^n$, yet this language is not context-free (you can see this by intersecting with $a^*b^*y^*$ to get the language of all words of the form $a^nb^ny^n$).