Anyone know about Insurance , ladies I need help with this issue !

My husband and I got married on feburary 19th, he tried adding me to his insurance so he sent a copy of our marriage certificate but they sent it back saying they couldn't accept it so he called to ask why and they told him they want the ORIGINAL one, not the one they gave us because the original one has a recorded #(or something like that)  . So , almost 2 months later we finally got it today! 

But the thing is , I already registered at another hospital because we got tired of waiting and to be prepared in case our baby came earlier . 

Okay so, with my husbands insurance he goes go a certain hospital and he asked me " do you want to change to (so and so) or do you want to stay at holy cross(where i'm already registered) I told him i'll stay where I am but my grandma told me that supposably theres a law that says when you have medical, that if you get insurance its a law to use the insurance before using the medical is this true ? our deduction at the hospital where my husband goes is only $100 &  my uncle said when he was married they used medical when they had insurance  and ended up having to pay over 1,000 dollars. 

Another question , since we faxed the original marriage certificate this morning, 

that would mean they recieved it today(same day) and since were married, will I be added to his insurance right away? 

Its kind of stressing to me because i'm due in a week and turn 39 weeks tommorow!