“The mother can stop the father seeing the children.”
This is something that the Courts try to address at a very early stage. Access is now known as contact. Contact is the right of the children, not the parents. The key thing to remember is that a child needs both parents and in all but the most exceptional circumstances, usually where there is a real risk of harm, the non-resident parent will get contact. Where a parent with residence is deliberately blocking contact, the Courts have a range of powers up to and including imprisonment of the parent stopping contact and removal of the children to the other parent.
Once a relationship is over the parents will often want nothing to do with each other, but if there are children they will almost inevitably have to continue to deal with each other. In the same way that the Courts will not tolerate anyone using contact as an opportunity to be abusive to their ex-partner, the Courts take a very active role where one parent is refusing to allow contact to the other.