Your husband needs to wake up and get himself to court. He absolutely DOES NOT need to even respond to a solicitors letter . They have absolutely no power to dictate how you /your husband behave. The only document that does this is an order from the court. Let her waste money getting her lawyer to write pointless letters . You can safely ignore them.
First he needs to fill in the application for a child arrangements order .
Follow the steps here
apply-to-court-about-child-arrangements.service.justice.gov.uk/steps/opening/start?
It costs £255 . He doesn't need a solicitor. Most people self represent unless he has a history involving criminal activity, violence and /or there is evidence of him being abusive. Which could make the application harder .
If there is no reason why he should not have a relationship with his child then just go ahead and apply. I am presuming he is named on the birth certificate ? He will be obliged to request mediation with ex but that can be signed off if she refuses.
There is no reason why your husband should not do this - in fact I would be pretty disappointed in any man who didn't fight for a relationship with his child. (In the basis he is a decent father)
If the fees are off putting just fill in the 'help with fees' form on the website.
By the way. No judge will make an order for a father to divorce his wife ! This is completely ridiculous.
In the worse case scenario - if the mother could produce irrefutable evidence that YOU have abused the children and were a risk to their welfare - then the order could require him to have contact at a place on his own - but in the normal scheme of things where you are just a normal non abusive partner - no judge will direct your husband to exclude you during his contact time.
What he does with the child, who he allows his child to have a relationship with, who he allows to spend time with his child is entirely his business in his court ordered time.