My girlfriend has been married for approx 5 years and was married outside of Canada, her husband is Canadian and they have a young child together, she is a US citizen and born in the US,they are now separated, he knows that we had a affair and this was ongoing whilst she was pregnant.
What does the law say about her rights as a mother towards that child as she is concerned about losing the child, she has told him she will live in the US but close o the border to unable him to see the child whenever he wants.

Please could you advise

The custody will be decided in the divorce.Under the law, the court must make a custody order consistent with the best interests of the child,
The judge may or may not consider the fact she is adulterer

Thanks for the answer what is her best course of action from here

Thanks for the answer what is her best course of action from here

She must prove that having an affair does not harm the child.
However, this also depends on the law of the state, the facts in each custody case and the personal bias of the judge.

Would a legal separation by the way too go with both of them signing there intent

Depends on the State - if they both are represented, come to a fair agreement, sign and file a S/A in some States that will be the grounds for divorce after a period.

What State?

If he knows she was having an affair while pregnant he may very well wonder if she was having an affair BEFORE she got pregnant, question the identity of the father and request DNA testing.

Identity is not in question and in fact DNA test was done, she will be living in VT and he will be in Montreal.

Does something legally have to be signed in both the US and Canada?

The reason she is concerned is that she would love for us to try and build a life together but is too scared currently as she does not know what impact this will have over her child.

What can she do to be sure everything is going to be OK, she has left him and does not wish to return to Canada

What is her residency? Where is she filing for divorce?