By having a DNA test done
the daughter
He has no rights until the child is born even if he can prove it is his.
someone`s daughter
If you have to file a claim on that child they can request that you 'prove' they are a full time student. I had to do this periodically without a claim while our daughter was in college. And if you cannot prove it that child will have no coverage.
Since you were adopted by another man at age 6 and now go by his surname I don't think you can be considered you biological fathers child in the eyes of the law now. Your biological fathers name is not on your birth certificate. You could try and see if social security would except a DNA sample from your biological fathers other children to prove that you are his child or maybe your biological fathers parents(this would be better) if any of them would do that for you.
your second cousin
your 5th cousin
If you have joint custody of your child and disagree re the fathers Day Care then you should try talking to him first and if that doesn't work then go to court. You have to prove that the child is truly in a harmful environment.
your 5th cousin
Your first cousin
daughter
You are his first cousin.