untrue. She can show Up that she is in relationship with the father and he can write this in the invite Letter that He invite her and him. And he never say that they son dont meet her before😉
and in the invite Letter your son can clearify everything in Detail. Also Show Up Pictures from you and your girlfriend. He have to write that you both are coming and he take care of all payments from her.
You have enough time for that to prepare. In total May you need 4 weeks. Not more. She will get a Schengen Visa for 30 days. Your son is then in charge that she really go back.
its Not possible to do it Like that. You have to be in Germany to prepare the Verpflichtserklärung. Its Not possible to do that at the embassy from Germany.
But there is another way and that could go easy for you. Ask your son to make the Verpflichtserklärung and the invite Letter for.the marriage for your girlfriend.
When the Finance from your son IS good IT will be No Problem