My brother and his girlfriend have a 5 year old and 2 year old. She is still legally married to another man. When the 5 year old was born, supposedly it was law that since she was indeed still married, her "husband's" name must be put on the birth certificate, not my brothers. With the 2 year old, I am not aware of who's name is on the certificate. My question is, is this indeed the case, in that the husbands name was to be written under father? A paternity test was done, but after that, not much else. What can be done in order to get my brother, their father, on the birth certificate?

Its impossible to say unless we know where this is going on. When persons are married and a birth of a child comes into the marriage the husband is the presumed legal father.

That being said the outcome of that can vary from state to state. Some states allow for a challenge and others do not.

We're in Ohio.
They (the girlfriend and her husband) have been separated for nearly 10 years, they just have never bothered to divorce. Couldn't she have left the name blank on the certificate?
(I appreciate your help!)

Often if married the law is that the husband is assumed the legal father.

Some states allow a legal challenge but most that do have a time limit where it is allowed.

She needs to move on, divorce, get the child either adopted by their legal father, or though court prove paternity and challenge the birth certificate.

And it is easy to know who is on the birth certificate, get a copy of it.

It looks like there is no time limit except if the child is 18 plus 5 years. That is the only limitation for a challenge.

Lawriter - ORC - Chapter 3111: PARENTAGE

As noted ANY question about law needs to include your general locale as laws vary by area. Most areas DO have laws that state when a child is born to a married couple the husband is the presumed father.