You did fine! If letting the other parent know that your child may need counseling or has to possibly go to the Dr., and they feel guilty about it, then so be it. If they feel guilty due to things that have to do with your children, then that is their issue to deal with.
Then again I can totally understand where Arsene's perspective is coming from as well. The thing is now, you can't take it back & it is water under the bridge, so move forth.