If without even knowing if he is actually the father, are we responsible for her maternity care or anything else before the baby born?

My husband had an affair and the girl is claiming she is pregnant with his baby despite being currently married herself. She has been slamming us on social media and keeps threatening him with bills etc. I spoke with domestic relations who said there was nothing to be done till the kid was here and paternity was established. However, her behavior worries me and I would like to be prepared for all things.