'there is no yet any ruling about the legal custody therefor I'm still hold the rights for my child whether i live in china or in the state next door.'
I agree with MomforTwo..........if you don't know US Family Law, you obviously don't know what your rights are in the US. No jurisdiction in this country will recognize you as a parent and give you equal legal rights until you obtain that through a US court, period. So basically the ONLY issue here is legal custody, who has it and who doesn't. Because the child and mother are in the US and you aren't.........and nothing has been established in a US court regarding legal custody of your case.......ONLY the mother is recognized as a legal parent to this child....to ANY entity.
But if you don't believe us, contact a family law atty., preferably in the state that the mother and child reside in, and ask them if you have any legal rights regarding the child. They will tell you the same thing.
'so far i have legal rights as a parent an till there is no court in any of both countries saying the contrary my child and both parents are protected under those same laws.' No, you do NOT......that is not how child custody works in the US, Hague Convention or not.
Let me try to explain it another way........even IF you were a US citizen and had a child out of wedlock, even then you would not have any rights to the child and say-so over what happens to him/her until you go to court and get it. Being a citizen of another country is no different.
Once you have joint legal custody established in the US, then and only then will you have the right to have a say on what happens to your child, regarding education, medical, and anything else that is included in the custody order. Then you can deal with the issue that brought you here in the first place. It's called 'getting your ducks in a row'......work on the issues in the order that they need to be addressed. FIRST, you need to establish legal custody in a US court, THEN you can address the vaccination issue when you have the legal voice to do so. We can't make it any plainer than that.