>Therefore i formulated: あなたが私のことをあなたの息子だと思うのが嬉しいDoes this make sense?
Yes, it is grammatically, syntactically correct and makes sense but it does not sound heart-warming.
Your sentence sounds like "Gaijin-like" or "European-language-translation-like" but it is no problem because you actually are.
And if I put a "language-soy-sauce" in your "translation-like" sentence to make it sound like heart-warming Japanese, like :
あなた → みなさん or お二人(because they are two)
あなたの → 自分の
思う → 思ってくれる,
that would be:
みなさんが私のことを自分の息子だと思ってくれて、とても嬉しい
お二人が私のことを自分の息子だと思ってくれて、とても嬉しい