I would not go to court as it could upset/annoy the mum more than she already is. In my mind you have no say in anything its between the parents of the children and best if you stay out of it. If you don't like contributing towards legal cost or whatever then say so to your boyfriend.

If my ex hubby had a girlfriend who thought she had a say in anything towards the children or even turned up at court I would ask her to leave as its nothing to do with her.

I am talking from an emotional point of view not a logical one, if you want to keep the peace I would not go.

This is just my thoughts.