What is the source of information for the German Embassy to say that (1) you are sapindas and (2) your marriage is not valid under the Hindu Marriage Act? Two are supposed to be in Sapinda relationship if they have a common ancestor counting 5 generations on the father's side and 3 generations up on the mother's side, counting the person himself as generation-1. In your case your father's father is a common ancestor. He 3 generations behind you. He is 4 generations behind your wife. As the connection is through her father's mother (more than 3) she is not your sapinda for the purpose of law.
If both of you were in sapinda relationship how could you register under the Hindu Marriages Act, 1955? The fact that you were able to register itself is enough evidence that you are legally married.
Under the Act sapinda marriages are not valid unless such marriages are customary in a community.
This is vague and ambiguous. Your married is not valid but the marriage of a similarly related couple from the South is valid. This is discrimination. You make representations to the embassy. It will be pertinent to find out who advises the embassy on such matters.
I suspect that you got married without the approval of your families and hence that your families are against you.